In Afro-Asiatic we have the feminine ending -a which has the following evolution history:
-a < -aha < -at < et
where ha is a glottal fricative.
In IE (for instance, in Russian, Greek, Latin) we also have the feminine ending -a which has the following history (classically):
-a < aha < eha
where ha is the a-coloring laryngeal.
Can we by analogy suppose that ha < t?
This gives a number of analogies between other PIE words:
haeuhaos <-> teutos (both "grandfather") (also haetos is reconstructed for "father" in PIE -> Russian otets)
(compare Proto-Afro-Asiatic haabbaha "father" here)
haequ- <-> tequ- (both "flowing water")
haecsom <-> tecsom (both "axe")
haecmon "stone" <-> tecsōn "builder"
haeĝos <-> teĝos (both "leader")
haersos <-> tersos (both "dry, e.g., land") (compare also Greek χερσος, "dry land")
How can it be explained?