The God of Abraham is the God of the Jew and the God of Christians. Islam claims this is also their god, but there are numerous differences. Islam sees Jesus as a Prophet, not part of the Triune God.
So if I'm reading your question correctly, yes, the God of Abraham is the same God to the Jew, the Islamist, and the Christian.
I seriously you suggest you read the Robert Spencer blogsite I referenced. I would ask your Islamist friends about the verses I cited.
I would also ask them about the following:
Here’s an interesting contrast between the peaceful Islam and the hateful Christianity:
The example of Mohamed on adultery Sahih Muslim, Book 17: 4206
There came to him (the Holy Prophet) a woman from Ghamid and said: Allah's Messenger, I have committed adultery, so purify me. He (the Holy Prophet) turned her away. On the following day she said: Allah's Messenger, Why do you turn me away? Perhaps, you turn me away as you turned away Ma'iz. By Allah, I have become pregnant. He said: Well, if you insist upon it, then go away until you give birth to (the child). When she was delivered she came with the child (wrapped) in a rag and said: Here is the child whom I have given birth to. He said: Go away and suckle him until you wean him. When she had weaned him, she came to him (the Holy Prophet) with the child who was holding a piece of bread in his hand. She said: Allah's Apostle, here is he as I have weaned him and he eats food. He (the Holy Prophet) entrusted the child to one of the Muslims and then pronounced punishment. And she was put in a ditch up to her chest and he commanded people and they stoned her. Khalid b Walid came forward with a stone which he flung at her head and there spurted blood on the face of Khalid and so he abused her.Allah's Apostle (may peace be upon him) heard his (Khalid's) curse that he had huried upon her. Thereupon he (the Holy Prophet) said: Khalid, be gentle. By Him in Whose Hand is my life, she has made such a repentance that even if a wrongful tax-collector were to repent, he would have been forgiven. Then giving command regarding her, he prayed over her and she was buried.
And now contrast Islam with the hateful Christianity:
The example of Jesus on adultery (John 8:1-11)
But Jesus went to the Mount of Olives. Early in the morning He came again into the temple, and all the people were coming to Him; and He sat down and began to teach them. The scribes and the Pharisees brought a woman caught in adultery, and having set her in the center of the court, they said to Him, "Teacher, this woman has been caught in adultery, in the very act. "Now in the Law Moses commanded us to stone such women; what then do You say?" They were saying this, testing Him, so that they might have grounds for accusing Him. But Jesus stooped down and with His finger wrote on the ground. But when they persisted in asking Him, He straightened up, and said to them, "He who is without sin among you, let him be the first to throw a stone at her." Again He stooped down and wrote on the ground. When they heard it, they began to go out one by one, beginning with the older ones, and He was left alone, and the woman, where she was, in the center of the court. Straightening up, Jesus said to her, "Woman, where are they? Did no one condemn you?" She said, "No one, Lord." And Jesus said, "I do not condemn you, either. Go. From now on sin no more."
Sheesh, why do you even waste your time comparing JESUS with mohammed?
Your knowledge is impressive and I respect it. Is it that you were a Muslim scholar and converted?? What you point out is very important to the discussion that never seems to happen. What is it that is luring so many to the Muslim religion??