PS

*-šVmV/-šVnV - their; them (genitive and accusative pronominal suffix, 3 pl.) (Kogan 2009:70)

The shift *š- > h is distributed between languages the same way as in the realm of independent pronouns of the 3rd person.
The plural of the pronominal suffix of the 3rd person is based on the element š- with the extension -m- or -n- combined with more or less expressed vocalic oppositions (Kogan 2009:69). The character of consonantal and vocalic oppositions in individual languages generally corresponds to the nominative forms.

Akkadian
-šina - their (genitive pronominal suffix, 3 fem. pl.) (GAG § 42 g)
Akkadian
-šunu - their (genitive pronominal suffix, 3 masc. pl.) (GAG § 42 g)
Arabic
-hum/-humu - their; them (genitive and accusative pronominal suffix, 3 masc. pl.) (Fischer 2002 § 268)
Arabic
-hunna - their; them (genitive and accusative pronominal suffix, 3 fem. pl.) (Fischer 2002 § 268)
Geez
-omu, -homu - their; them (genitive and accusative pronominal suffix, 3 masc. pl.) (CDG 218, Bulakh–Kogan 2013b:101)
-homu is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.
Geez
-on, -hon - their; them (genitive and accusative pronominal suffix, 3 fem. pl.) (CDG 218, Bulakh–Kogan 2013b:101)
-hon is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.
Tigre
-om/-hom - their; them (genitive and accusative pronominal suffix, 3 masc. pl.) (Bulakh–Kogan 2013b:101, WTS 6)
-hom is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.
Tigre
-an/-han - their; them (genitive and accusative pronominal suffix, 3 fem. pl.) (Bulakh–Kogan 2013b:101, WTS 17)
-han is the allomorph used with verbal forms ending in *-ā (the etymological guttural is restored). See Bulakh–Kogan 2013b:105.
Tigrinya
-om - their; them (genitive and accusative pronominal suffix, 3 masc. pl.) (Bulakh–Kogan 2013b:101)
-ˀom with verbal forms ending in *-ā (the glottal stop is of secondary nature, see Bulakh–Kogan 2013b:105).
Used as a polite form (Bulakh–Kogan 2013b:106).
Tigrinya
-än - their; them (genitive and accusative pronominal suffix, 3 fem. pl.) (Bulakh–Kogan 2013b:101)
-ˀän with verbal forms ending in *-ā (the glottal stop is of secondary nature, see Bulakh–Kogan 2013b:105).
Used as a polite form (Bulakh–Kogan 2013b:106).
Jibbali
-hum - their; them (genitive and accusative pronominal suffix, 3 masc. pl.) (Johnstone 1975:118)