Geez

-o, -hu - him (accusative pronominal suffix, 3 masc. sg.) (Bulakh–Kogan 2013b:101)

-hu is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.

PS
*-šū̆ - his; him (genitive and accusative pronominal suffix, 3 masc. sg.) (Kogan 2009:69)
The shift *š- > h is distributed between languages the same way as in the realm of independent pronouns of the 3rd person.