I'm sorry, I don't understand what you just said or why you think it is wrong.
Muslims, Jews, and Christians all believed that there was an Abraham and that God called him to go to a new land and made a promise to him. All three religions believe this story. The same God. At this point, however, the religions begin to diverge. Muslims believe that Ishmael (Abrahams illegitimate firstborn) was actually the true heir to God's blessings, while Jews and Christians believe it was Isaac. Later on Christianity diverges from Judaism when the Messiah, Christ, appeared.
If you believe that the God of the Jews is the same as our God, then you must concede that the God of the muslims is also the same God. It's just a very warped view and interpretation of who God is.