Tax-Free Fixed Income Fund III for Puerto Rico Residents N-CSR Certified annual shareholder report (management investment company)

Exhibit 13(b)(1)

Carlos V. Ubiñas and William Rivera, of Tax-Free Fixed Income Fund III for Puerto Rico Residents, Inc. each certify that:

1.       This Form N-CSR filing for the Fund (the “Report”) 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
	President
By:	/s/ William Rivera
	William Rivera
	First Vice President and Treasurer
Date:	September 9, 2021