Exhibit (a)(1)(iv)

Form of Letter from the Fund to Shareholders

in Connection with the Fund’s Acceptance of Shares

APOLLO S3 PRIVATE MARKETS FUND

c/o SS&C GIDS, Inc.

PO Box 219536

Kansas City, MO 64121-9536

[DATE]

[SHAREHOLDER NAME/ADDRESS]

Dear Shareholder:

This letter serves to inform you that Apollo S3 Private Markets Fund (the “Fund”) has received and accepted for purchase your tender of shares of beneficial interest in the Fund.

In accordance with the terms of the tender offer, you will be issued a non-interest bearing, non-transferable promissory note (the “Note”), which will be held on your behalf by SS&C GIDS, Inc., the Fund’s transfer agent (the “Transfer Agent”), entitling you to receive payment(s) in an aggregate amount equal to the net asset value of the tendered shares as of September 30, 2025.

If you have any questions (or wish to request a copy of your Note), please contact the Transfer Agent at 1-888-926-2688.

Sincerely,

Apollo S3 Private Markets Fund