It is definitely canon for Islam that Jews and Christians believe in the same God, except they got a bunch of stuff wrong. They basically see themselves as Monotheism v3.0.I'm more interested in a slightly different questions: Do the several Abrahamic faiths believe, either as canon, or as a commonly held belief (I'm presenting those as distinct questions) that they believe in the same God?
It is currently the opinion of the Catholic Church that Muslims believe in the same God they do, except they're getting a bunch of stuff wrong. They also hold that Jews believe in the same God they do, but now God has changed his mind on some things and the Jews refuse to acknowledge that.
I'm not sure how Judaism and other Christian churches see things. It probably varies a bunch.