Michael Williams points out that in official Catholic doctrine, Christians and Muslims worship the same God, but Michael disagrees. I think before you can really answer this question, you have to understand what "being the same" is, and it's not as simple as you might think especially as regards distant objects.
Suppose that you and I are talking about a historical figure, say Aristotle. We have some different beliefs about Aristotle. I believe that he wrote the Metaphysics and you don't. I believe that he was Greek but you believe that he was Macedonian. I believe that he was a student of Plato but you don't. Are we talking about the same man? Yes, but we just believe different things about him.
Now lets go further. I believe that Aristotle was known in Athens before he became Alexander's teacher, but you believe that he was just a con man who fooled a Macedonian king into thinking he was a respected philosopher. You have this theory about how he claimed most of the writings of an obscure student of Plato as his own and used his political power to create his historical reputation. According to you, Aristotle never wrote anything that I think he wrote.
Are we still talking about the same man? Well, if I'm right, then we are. But if you are right, then it's not so clear. When I talk about Aristotle, then I'm talking about the man who was a student of Plato and who wrote all of Aristotle's books, not the man who taught Alexander. Almost everything I have to say about Aristotle applies to this unnamed student of Plato and none of it to the guy named Aristotle who taught Alexander the Great.
But we are still talking about the same Aristotle. Aristotle is not identified by his writing. The name "Aristotle" does not have the same connotation as the description "the man who wrote the books commonly attributed to Aristotle". Rather, "Aristotle" is a name that takes its meaning from a historical chain of references.
Some guy who actually knew Aristotle, teacher of Alexander, mentioned him to some guy who didn't know Aristotle. The first guy was wrong in thinking that this teacher of Alexander wrote the Metaphysics, but he was still referring to someone he knew. The second guy gets this historical reference from the first guy and passes it to a third, and so on down through the ages (through both speech and writing) until I use the term myself. You're own usage of the term shares a history with mine so we are talking about the same man named Aristotle, it's just that I have some false beliefs about him that were passed down along with the reference.
A technical way to say this is that the denotation of a name (the thing the name "points to") is defined by the historical usage of the name. This is one way in which names are different from descriptions which usually denote something that satisfies the description.
When Mohammed preached about Allah, if he intended his hearers to understand that he was talking about the God of Abraham (as I believe he was) then he was using a name with a history, a history shared by our word "God". Therefore the two names denote the same Being, even if one of them is associated with a truckload of false ideas.