Exhibit 19(b)

This certification is furnished pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. §1350, and accompanies the report on Form N-CSR for the period ended August 31, 2026 (the “Report”), of the Puerto Rico Residents Tax-Free Fund III, Inc. (the “Fund”).

Carlos V. Ubiñas and José Grau of the Fund each certify that:

1.   This Form N-CSR filing for the Fund fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2.   The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Fund.

 

By:		/s/ Carlos V. Ubiñas
		Carlos V. Ubiñas
		Principal Executive Officer

 

By:		/s/ José Grau
		José Grau
		Principal Financial Officer

Date:  November 5, 2026