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.

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.