Israel and the Arab nations trace their ethnic origins to Abraham.
Islam ( Islam means Submission ) has an origin far removed from Abraham's time. The founder of Islam , Mohammed, appeared some 2300 years later than Abraham I think. As far as I know there are no ancient documents before 300 AD that link Mohammed to Abraham ( approx 2000 BC ) .
Writings from the time of Moses ( 1400 BC ) indicate a link between Abraham and Israel.
It could be that somebody speaks with a forked tongue. I'll leave that for you to work out.
Whether the god of Israel is identical to the god of Islam is a subject that people have written large and learned articles on, I don't think we could settle that here.
