There is only one God - the Muslims worship Him incorrectly and ascribe to Him actions which He has not undertaken and assign attributes to Him which He does not possess.
My personal belief is that the Koran is the work of a demon who appeared to/possessed Mohammed.
That's why the Koran is such a clever mix of truth (that God is one, is merciful, will judge the world, chose Abraham for himself, etc.) and fiction (that Jesus was only a prophet, that Mohammmed was also a prophet, that there is a new revelation after Jesus, etc.)
If the God they worship, the violent one who gives virgins to murderers, doesn't actually exist. Do prayers somehow migrate to the One True God, or are they in a sense simply worship intangible idols? (or worse real demons)?
According to the CCC, its the same God though worshiped wrongly, and sinfully.
According to my Orthodox Priest, they don't really worship the same God.