This theory is baseless and has been debunked comprehensively - and I give a link at the end to one such comprehensive treatment of this theory. Full references are given there for the information below.
In this post, I just want to extract some highlights that show categorically that Allah of the Quran is the same God/Yahweh/YHWH of the Bible.
First, note that pre-Islamic Arabic speaking Christians and Jews referred to God as Allah. Christians baptised sons with the name 'Abdullah' (slave/servant of Allah) - incidentally also the name of Muhammad's, pbuh, father. To this day, Arabic speaking Christians and Jews refer to God as Allah and is what is in Arabic Bibles.
Now, let's turn to the Quran and the categoric statements on the subject:
(Quran, 29:46)Do not argue with the People of the Book [the Jews and Christians] except in the kindest possible manner, save those of them who are oppressive, and say: “We believe in what was revealed to us and what was revealed to you; our God and your God are one and the same, and to Him do we submit ourselves.”
The Quran offers religious criticisms of Judaism and Christianity, each time referencing Allah as the God of the Jews and the Christians. For example, the Quran says:
(Quran, 9:30)The Christians say, “The Christ is Allah’s son.” Such are the sayings which they utter with their mouths!
There exists a multitude of Quranic verses that associate the Allah of Islam with God the Father of Christianity. In yet another verse, for instance, Jesus says:
(Quran, 5:72)“O Children of Israel! Worship Allah my Lord and your Lord.”
The Quran says clearly that Noah was a Prophet of Allah, for example - but most tellingly, this verse about Abraham shows that the God of the Quran (Allah) is not a pagan moon-god:
(Quran, 6:76-79)When the night grew dark over him he saw a star and said, “This is my Lord,” but when it set, he said, “I do not like things that set.” And when he saw the moon rising he said, “This is my Lord,” but when it too set, he said, “If my Lord does not guide me, I shall be one of those who go astray.” Then he saw the sun rising and cried, “This is my Lord! This is greater.” But when the sun set, he said, “My people, I disown all that you worship beside Allah. Behold, I have turned my face as a true believer towards Him who created the heavens and the earth. I am not one of the idolaters.”
http://www.loonwatch.com/2011/08/the-al ... t-page-iv/
Cheers,
Shafique