Because it surfaces as /h/ in Tuareg and disappears in most Northern dialects with compensatory lengthening of preceding short vowels. Intervocalically it sometimes surfaces as /ww/ or /ggʷ/ in Northern dialects though. In Ghadames it is /β/ and in Awjili it is /v/, and for some dissimilatory patterns it clearly behaves as a labial (patterning with /m/, /f/ and /b/), which seems difficult to explain if it were *h. Therefore all still living historical linguists of Berber I think are in agreement that *β was some kind of labial. :-)

*β almost certainly goes back to *b at an earlier point (Proto-Berber has very few compelling examples for a *b, so there's a gap in the system there). Also some good cognates with Afro-Asiatic languages seem to suggest it's a *b!

I would love for your to enlighten me what those rules might be. As far as I can tell, the alternation is basically random in the Quran. In inscription and papyri from around the same period رحمت الله is almost the exclusive selling.