Geez

-ā, -hā - her (genitive and accusative pronominal suffix, 3 fem. sg.) (CDG 213, Bulakh–Kogan 2013b:101)

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

PS
*-šā̆ - her (genitive and accusative pronominal suffix, 3 fem. 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.