Muslims believe in the same god as Christians do. This is a common mantra I hear spouted by Muslims. They make the racist assumption that if I'm white I must be a Christian so they think this argument has resonance with me. It doesn't. Firstly because I don't believe in any gods and secondly because I don't believe that imaginary characters imagined by different people at different times have the same characteristics just because they have the same character name or backstory.
Take Batman for example. There is a hell of a difference between the Batman played on the television in the 1960s when I was a child, the camp but sexless Batman of Adam West and the dark brooding menacing figures imagined by the likes of Tim Burton. Some Batman figures are all action vigilantes and others are just barely repressed homo-erotica. Just because he answers to the names of Batman and millionaire Bruce Wayne with a dark history of personal loss behind him it does not make him the same character.
There are far more god characters than there are Batmans, Robin Hoods or James Bonds. There are also far more heavens and hells than there are batcaves and 221 B Baker Streets and far more Satans than there are Jokers and Blofelds. There are at least as many imaginary one and only gods as there are monotheists to imagine them.
The character of god differs significantly between chapters in the same book of the old testament let alone between the god of Christianity and the god of Islam. There is no way that you can reconcile the god of the modern philosopher with his omnipotence and omniscience with the god who was walking in a different part of the garden when Adam took a bite of the wrong fruit.
Having the same character name and common themes in the backstory does not make a single God of Abraham. Some one and only gods are absolute monsters and others would be almost decent enough to be considered human. But at least I can say that none of them are my god, I never did like that fantasy fiction franchise, I prefer Doctor Who.