Thanks for the answer, but now I wonder why the Hebrew original of the name Amram was maintained in the Arabic translation whereas the Hebrew name "Abraham" was transferred into Arabic as "Ibraheem". 
My guess would be that "Abraham" was adopted/inherited in Arabic at an earlier stage (so it was phonetically adapted), while Amram - which is probably not a common name among Arabs - was transliterated more faithfully from the Hebrew when the Bible was translated.
I wouldn't worry too much about vowel shifts in the Semitic languages. They can vary within the same language both at the same time (various dialects with various pronunciations) and throughout history (diachronically). As an example for the later type of variation, the name of the Theotokos appears transcribed as
Mariam both in the Septuagint (the sister of Moses) and the NT, reflecting the earlier Jewish pronunciation. At a later stage the
a in the initial unstressed syllable was closed to
i, so now the Jews read
Miriyam. There are other examples of this and other such vowel mutations in Hebrew.
As far as regional/dialectic pronunciations are concerned, Sephardic and modern Israeli Jews would pronounce
Avraham, while the Ashkenazi (Teymani/Yemenite Jews as well) say
Avrohom (which became
Avrum in Yiddish), etc. The same variation occurs in Syriac: it's
Avrohom in the Western (Jacobite) dialects and
Avraham in the Eastern (Nestorian).