"Allah" does not mean "God of Abraham". Allah was the name of a local Arabian moon god. The Arabic word for the God of the Jews was "adonah" - an Arabicization of "Adonai", a Hebrew/Aramaic name for God.
Mohammed preached that this moon god was actually the only God and that Abraham worshipped Allah. He told Arabs that they were the true descendents of Abraham and that the Jews were liars and descendents of pigs and monkeys.
There is a reason why a crescent moon is the symbol of Islam to this day - it shows the true provenance of Allah. Fascinating, isn't it, that Islam forbids making an image of anything created - yet adopts an image of the moon as its symbol? Even more interesting that Muslims worldwide are expected to travel to Mecca at least once to do obeisance to a black stone - yet they claim that Christians are blasphemers and idolaters for worshipping Christ.
Look, linguistics is just not your area. Please see the following from the Catholic Encyclopedia about the Hebrew word for God used in the OT. (I assume you don't think the CE is overrun with PCness.)
"Elohim has been explained as a plural form of Eloah or as plural derivative of El. Those who adhere to the former explanation do not agree as to the derivation of Eloah. There is no such verbal stem as alah in Hebrew; but the Arabist Fleischer, Franz Delitzsch, and others appeal to the Arabic aliha, meaning "to be filled with dread", "anxiously to seek refuge", so that ilah (eloah) would mean in the first place "dread", then the object of dread. Gen., xxi, 42, 53, where God is called "the fear of Isaac", Is., viii, 13, and Ps. lxxv, 12, appear to support this view."
All other Semitic peoples used a form of "el" as a title for their gods. The Hebrew word Adonai is most often translated as Lord, not God. El, elohim and adonai are all titles, anyway. In the OT the personal name of God is YHWH.
Some Imams have tried to say this but tracing entemology of words and study of ancient Sumerian hyroglyphs pretty much disproves it. That an Arab would claim to be heir to any monotheistic religion prior to Mohammed is laughable anyway.