Exhibit 32.2

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350, AS ADDED BY

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Hudson Executive Investment Corp. III (the “Company”) on Form 10-K for the period ended December 31, 2021, as filed with the Securities and Exchange Commission (the “Report”), I, Ira Mosberg, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as added by § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) To my knowledge, the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the period covered by the Report.

Date: March 31, 2022	By:	/s/ Ira Mosberg
		Ira Mosberg
		Chief Financial Officer (Principal Financial and Accounting Officer)