Exhibit 10.1

INMUE BIO INC.

225 NE Mizner Blvd., Suite 640 

Boca Raton, Florida 33432

June 29, 2026

To the Holder of April 2024 Common Stock Purchase Warrants

Dear Holder:

INMUNE BIO INC. (the “Company”) is pleased to offer (this “Inducement Offer”) to you (“Holder”, “you” or similar terminology) the opportunity to exercise 50% of the existing Warrant to Purchase Shares of Common Stock issued to you on April 24 and April 29, 2024, as amended on December 22, 2025 (the “Warrants”), for a reduced exercise price equal to $1.40 (reduced from $1.95), and to amend the Warrant such that the maturity date of the warrant, as it relates to the remaining 50% of the Warrant, shall be extended from June 30, 2026 to December 31, 2027. The issuance, or resale, of shares of Common Stock underlying the Warrant have been registered pursuant to an effective registration statement (File No. 333-254221). The shares of Common Stock underlying the Warrant are referred to herein as the “Warrant Shares” and the registration statement referenced in the foregoing sentence is referred to herein as the “Registration Statement.” The Registration Statement is currently effective and, upon exercise of 50% the Warrant pursuant to this letter agreement (the “Inducement Agreement,” and together with the Second Amendment to Warrant to Purchase Shares of Common Stock (as defined below), the “Transaction Documents”), will be effective for the issuance or resale of the Warrant Shares, as applicable. Capitalized terms not otherwise defined herein shall have the meanings set forth in the Second Amendment to Warrant to Purchase Shares of Common Stock (as defined hereinafter).

The Company is making you this offer during the period from the date of this Inducement Offer set forth above and until 5:00 pm, Eastern Time, on June 30, 2026 (the “Exercise Period”). Exercise of 50% of the Warrant may be made during the Exercise Period by delivery to the Company of a duly executed facsimile copy or PDF copy submitted by e-mail (or e-mail attachment) of the Notice of Exercise attached to the Warrants, as applicable; provided, that the exercise of 50% the Warrant will be accompanied by payment in full of the Reduced Exercise Price (as defined below) to the Company and that The Holder will execute and return the Form of the Second Amendment to Warrant to Purchase Shares of Common Stock to the Company, together with the Amendment Consideration, no later than June 30, 2026, by 5:00pm, Eastern Time.

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The Company desires to reduce the Exercise Price (as defined in the Warrants) of the 50% of the Warrant held by each Holder (the “Reduced Warrants”) to $1.40 per share of Common Stock (the “Reduced Exercise Price”). In consideration for the Reduced Exercise Price and exercising the Reduced Warrants held by Holder pursuant to the terms of this Inducement Offer (the “Warrant Exercise”), the Company hereby offers to amend the Warrant to extend the maturity date of the remaining Warrants (other than the Reduced Warrants) from June 30, 2026 to December 31, 2027, which such amendment shall be substantially in the form as set forth in Exhibit A hereto (the “Second Amendment to Warrant to Purchase Shares of Common Stock”).

Notwithstanding anything herein to the contrary, in the event that any Warrant Exercise would otherwise cause the Holder to exceed the beneficial ownership limitations (“Beneficial Ownership Limitation”) set forth in Section 2(d)(viii) of Warrant (or, if applicable and at the Holder’s election, 9.99%), the Company shall only issue such number of Warrant Shares to the Holder that would not cause the Holder to exceed the maximum number of Warrant Shares permitted thereunder, as directed by the Holder, with the balance to be held in abeyance until notice from the Holder that the balance (or portion thereof) may be issued in compliance with such limitations, which abeyance shall be evidenced through the Warrants which shall be deemed prepaid thereafter (including the payment in full of the exercise price), and exercised pursuant to a Notice of Exercise in the Warrant (provided no additional exercise price shall be due and payable). The parties hereby agree that the Beneficial Ownership Limitation for purposes of the Warrant is as set forth on the Holder’s signature page hereto.

Expressly subject to the paragraph immediately following this paragraph below, Holder may accept this offer by signing this letter below and the Form of the Second Amendment to Warrant to Purchase Shares of Common Stock, which constitutes the Holder’s acceptance to exercise 50% of the Warrant at the Holder’s own discretion subject to the Beneficial Ownership Limitation set forth in Section 2(d)(viii) of the Warrant.

The Company agrees to the representations, warranties and covenants set forth on Annex A attached hereto as of the date hereof and as of the Closing Date.

The Holder represents and warrants that, as of the date hereof, the Holder is fully aware of, and has reviewed all of the Company’s public filings.

Holder represents and warrants that, as of the date hereof it is, and on each date on which it exercises any New Warrants it will be, an “accredited investor” as defined in Rule 501 of Regulation D promulgated under the Securities Act of 1933, as amended (the “Securities Act”).

If this offer is accepted and the transaction documents are executed, the Company shall issue a press release and/or file a Current Report on Form 8-K with the Commission disclosing all material terms of the transactions contemplated hereunder, including this letter agreement as an exhibit thereto with the Commission. From and after the issuance of such press release or filing of such Current Report on Form 8-K, as applicable, the Company represents to you that it shall have publicly disclosed all material, non-public information delivered to you by the Company, or any of its respective officers, directors, employees or agents in connection with the transactions contemplated hereunder. Notwithstanding the foregoing, the Company shall not publicly disclose the name of any Holder, or include the name of any Holder in such press release or Current Report on Form 8-K, without the prior written consent of such Holder. In addition, effective upon the issuance of such press release and/or filing of such Current Report on Form 8-K, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its Subsidiaries or any of their respective officers, directors, agents, employees or Affiliates on the one hand, and you and your Affiliates on the other hand, shall terminate.

No later than the third (3^rd) Trading Day following the date hereof, the closing (“Closing”) shall occur at such location as the parties shall mutually agree. The date of the Closing of the exercise of the Existing Common Warrants shall be referred to as the “Closing Date”.

[Holder Signature Page Follows]

Accepted and Agreed to:

Name of Holder: _________________________________________________________

Signature of Authorized Signatory of Holder: ______________________________________________________

Name of Authorized Signatory: ______________________________________________________

Title of Authorized Signatory: _____________________________________________________

Number of Warrants: _____________________________

Aggregate Warrant Exercise Price at the Reduced Exercise Price being exercised contemporaneously with signing this letter agreement: ________________________________________________________________________

Existing Common Warrants Beneficial Ownership Blocker: 4.99% or 9.99%

DTC Instructions: _________________________________________________

[Holder Signature Page]

FORM OF AMENDMENT TO WARRANT

This Second Amendment to Common Stock Purchase Warrant (this “Amendment”) is entered into and shall become effective as of the date on which INmune Bio Inc. a Nevada corporation (the “Company”) receives both (i) payment of the Amendment Consideration (as defined below) and (ii) a duly executed copy of this Amendment from the undersigned holder (“Holder”) (such date, the “Effective Date”).

WHEREAS, the Holder is the holder of that certain warrant issued by the Company to the Holder on April 24 or April 29, 2024 (the “Warrant”);

WHEREAS, the Company and the Holder desire to amend the Warrant as more particularly set forth below in exchange for the Amendment Consideration; WHEREFORE, the parties do hereby agree as follows:

1. The portion of the Warrant’s first paragraph:

“and on or prior to 5:00pm (New York City time) on June 30, 2026,”

is hereby amended and replaced with the following:

“and on or prior to 5:00pm (New York City time) on December 31, 2027”

2. As consideration for this Amendment, the Company has granted the Holder the option to exercise 50% of the warrant for a reduced exercise price of $1.40 per share of Common Stock and the Holder elected to exercise 50% of the warrant for such reduced price and has paid the Company such reduced exercised price (the “Amendment Consideration”). The effectiveness of this Amendment is expressly conditioned upon the Company’s receipt of the full Amendment Consideration.

3. The Holder must execute and return this Amendment to the Company, together with the Amendment Consideration, no later than June 30, 2026 (the “Execution Deadline”). If the Holder does not execute and return this Amendment, together with the Amendment Consideration, to the Company by the Execution Deadline, this Amendment shall be null and void and of no force or effect.

4. Except as expressly amended herein, all terms and conditions of the Warrant shall remain in full force and effect.

5. This Amendment shall be governed by and construed in accordance with the laws governing the Warrant.

6. This Amendment may be executed in counterparts, each of which shall be deemed an original, and shall be binding upon all parties, their successors and assigns, and all of which taken together shall constitute one and the same Amendment. A signature delivered by facsimile or email shall constitute an original.

[Signature Page Follows]

Annex A

Representations, Warranties and Covenants of the Company. The Company hereby makes the following representations and warranties to the Holder:

a) Subsidiaries. All of the direct and indirect subsidiaries of the Company are set forth on the SEC Reports (as hereinafter defined). The Company owns, directly or indirectly, all of the capital stock or other equity interests of each subsidiary free and clear of any liens, and all of the issued and outstanding shares of capital stock of each subsidiary are validly issued and are fully paid, non-assessable and free of preemptive and similar rights to subscribe for or purchase securities.

b) SEC Reports. The Company has filed all reports, schedules, forms, statements and other documents required to be filed by the Company under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), including pursuant to Section 13(a) or 15(d) thereof, for the two years preceding the date hereof (or such shorter period as the Company was required by law or regulation to file such material) (the foregoing materials, including the exhibits thereto and documents incorporated by reference therein “SEC Reports”). As of their respective dates, the SEC Reports complied in all material respects with the requirements of the Exchange Act and none of the SEC Reports, when filed, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading except as otherwise noted in a subsequent SEC Report. The Company has never been an issuer subject to Rule 144(i) under the Securities Act.

c) Organization and Qualification. The Company is an entity duly incorporated or otherwise organized, validly existing, under the laws of Nevada, in good standing under the laws of the Nevada, with the requisite power and authority to own and use its properties and assets and to carry on its business as currently conducted. The Company is not in violation nor default of any of the provisions of its certificate or articles of incorporation, bylaws or other organizational or charter documents. The Company is duly qualified to conduct business and is in good standing as a foreign corporation or other entity in each jurisdiction in which the nature of the business conducted or property owned by it makes such qualification necessary, except where the failure to be so qualified or in good standing, as the case may be, could not have or reasonably be expected to result in Material Adverse Effect (as defined below).

d) Authorization; Enforcement. The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this letter agreement and otherwise to carry out its obligations hereunder. The execution and delivery of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby have been duly authorized by all necessary action on the part of the Company and no further action is required by the Company, its board of directors or its stockholders in connection herewith. This letter agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms, except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

d) No Conflicts. The execution, delivery and performance of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate or articles of incorporation, bylaws or other organizational or charter documents; or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any liens, claims, security interests, other encumbrances or defects upon any of the properties or assets of the Company in connection with, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which such Company is a party or by which any property or asset of the Company is bound or affected; or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected, except, in the case of each of clauses (ii) and (iii), such as could not have or reasonably be expected to result in a material adverse effect upon the business, prospects, properties, operations, condition (financial or otherwise) or results of operations of the Company, taken as a whole, or in its ability to perform its obligations under this letter agreement.

e) Trading Market. The transactions contemplated under this letter agreement comply with all the rules and regulations of Nasdaq.

f) Filings, Consents and Approvals. The Company is not required to obtain any consent, waiver, authorization or order of, give any notice to, or make any filing or registration with, any court or other federal, state, local or other governmental authority or other Person in connection with the execution, delivery and performance by the Company of this letter agreement, other than: (i) the filings required pursuant to this letter agreement.

g) Material Changes; Undisclosed Events, Liabilities or Developments. Since the date of the latest audited financial statements included within the SEC Reports, (i) there has been no event, occurrence or development that has had or that could reasonably be expected to result in a Material Adverse Effect, (ii) the Company has not incurred any liabilities (contingent or otherwise) other than (A) trade payables and accrued expenses incurred in the ordinary course of business consistent with past practice and (B) liabilities not required to be reflected in the Company’s financial statements pursuant to GAAP or disclosed in filings made with the Commission, (iii) the Company has not altered its method of accounting, (iv) the Company has not declared or made any dividend or distribution of cash or other property to its stockholders or purchased, redeemed or made any agreements to purchase or redeem any shares of its capital stock and (v) the Company has not issued any equity securities to any officer, director or Affiliate, except pursuant to existing Company stock incentive plans. The Company does not have pending before the Commission any request for confidential treatment of information. Except for the issuance of the Securities contemplated by this Agreement or as set forth on the SEC Reports, no event, liability, fact, circumstance, occurrence or development has occurred or exists or is reasonably expected to occur or exist with respect to the Company or its Subsidiaries or their respective businesses, prospects, properties, operations, assets or financial condition that would be required to be disclosed by the Company under applicable securities laws at the time this representation is made or deemed made that has not been publicly disclosed at least 1 Trading Day prior to the date that this representation is made. For purposes hereof, “Material Adverse Effect” means (i) a material adverse effect on the legality, validity or enforceability of the Transaction Documents, (ii) a material adverse effect on the results of operations, assets, business, prospects or condition (financial or otherwise) of the Company and the subsidiaries, taken as a whole, or (iii) a material adverse effect on the Company’s ability to perform in any material respect on a timely basis its obligations under any Transaction Document.

h) Listing and Maintenance Requirements. The Common Stock is registered pursuant to Section 12(b) or 12(g) of the Exchange Act, and the Company has taken no action designed to, or which to its knowledge is likely to have the effect of, terminating the registration of the Common Stock under the Exchange Act nor has the Company received any notification that the Commission is contemplating terminating such registration. Except as set forth on the SEC Reports, the Company has not, in the 12 months preceding the date hereof, received notice from any Trading Market on which the Common Stock is or has been listed or quoted to the effect that the Company is not in compliance with the listing or maintenance requirements of such Trading Market. The Company is, and has no reason to believe that it will not in the foreseeable future continue to be, in material compliance with all such listing and maintenance requirements. The Common Stock is currently eligible for electronic transfer through the Depository Trust Company or another established clearing corporation and the Company is current in payment of the fees to the Depository Trust Company (or such other established clearing corporation) in connection with such electronic transfer.