The God of Abraham, the Creator of everything is NOT the same as the god of the Muslims.
They differ in character and attributes therefore cannot be one and the same. God cannot be divided against Himself.
E.g.
The God of Abraham swears by Himself as there is no-one or no thing higher. Heb 6:13
13 "For when God made a promise to Abraham, because He could swear by no one greater, He swore by Himself, "
Allah swears by the sun, moon and stars, and other created entities.