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.

Akkadian
-ša - her (genitive pronominal suffix) (GAG § 42 g)
In Akkadian there is a vocalic opposition between genitive and accusative forms of 3 fem. sg. pronominal suffixes. See -ši.
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.
Tigre
-a/-ha - her (genitive and accusative pronominal suffix, 3 fem. sg.) (Bulakh–Kogan 2013b:101, WTS 1)
-ha is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.
Tigrinya
-a - her (genitive and accusative pronominal suffix, 3 fem. sg.) (Bulakh–Kogan 2013b:101)
-ˀa with verbal forms ending in *-ā (the glottal stop is of secondary nature, see Bulakh–Kogan 2013b:105).