I've always understood that Mohammed was said to have received a new message from the 'old' God of the Torah. Much in the sense that the God of Christianity is the same God of Judaism but with the New Testament added.
However, Christians and Jews do not believe the Koran to be actually God-inspired, and thus do not believe Allah is the true God.
Much in the same way that Jews do not believe Christians to be following the true God because they don't believe Jesus or the New Testament to be of God.

__________________

Bomber's Notebook | Secrets of the Minish Cap Library | Theorizing Resources | Aralith's OoT Retelling
Voted as Best Zelda Theorist in the Summer '08 Awards. Thank you to all who voted, and to all who inspired me along the way!