Abraham is called Ibrahim by Muslims. They see him as the father of the Arab people as well as the Jewish people through his two sons, Isaac and Ishmael (Isma'il in Arabic).
Indeed Muslims believe & worship the one true God of Jacob, Isaac, Abraham, Noah, & Adam. The Koran clearly praises Abraham for disbelieving in the deity of the moon & only believing the one true God!
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They do not worship the moon god!
Muslims believe in the God of Abraham and Ishmael. Christians and Jews came before Muslims. Basically Judaism and Christianity trace their heritage through Abraham’s son Isaac, and Muslims trace their heritage through another son, Ishmael, who was sent away from Canaan (where Abraham lived) with his mother, Hagar, after Isaac was born.
The Muslims believe they are specifically descendant from Ishmael, Abraham's first son. Thus the line of Isaac and the line of Ishmael continue to fight over the Holy Land.