Factually incorrect.
Muslims worship Allah who was originally a pagan moon good; the Christian god was never a pagan moon god. Mohammed repurposed Allah as the sole deity - it was easier for him than making up a new god.
Islam doesn't have Jewish roots. The Koran is the literal word of Allah. (It is curious, however, that bits of the Koran seem to be based upon badly remembered parts of Jewish scripture. It's almost as if Mohammed wanted the Jews to accept him as their prophet which, of course, is why Mohammed, when the Jews of the Banu Qurayza refused to accept him as such, had all the teenage boys and men slaughtered and the women and children taken as slaves and sex slaves.)