Akkadian

-šu - his; him (genitive and accusative pronominal suffix, 3 masc. sg.) (GAG § 42 g)

Sargonic orthography distinguishes between genitive -SU and accusative SU₄.

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.