EXHIBIT 32.2

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned, David K. Spohr, Senior Vice President and Director of Fund Administration of Preferred Investment Solutions Corp., the Managing Owner of World Monitor Trust III – Series H (“Registrant”), hereby certifies pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) Registrant’s Annual Report on Form 10-K for the period ended December 31, 2006, as filed with the Securities and Exchange Commission on the date hereof (the “Annual Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/s/ David K. Spohr

David K. Spohr

Senior Vice President and Director of Fund Administration

(Principal Financial/Accounting Officer)

March 30, 2007