To get a clear answer, Judaism should be accounted. If Christians claim they worship the same God of Judaism, the God if Adam, Noah, Abraham and Moses, the God Who does not change, then easy to say, Muslims and Christians worship the same God. If answer is no for the God of Judaism, then it is same for the Muslims.
A answer in Judaism.SE may help- http://judaism.stackexchange.com/a/14501/1712
Update: As the OP himself has questioned about the substance matter of this answer, I feel to clarify my answer adding few more words.
We can see, from this page of answers, that the answer to the question "whether Christians and Muslims worship the same God" has a dual nature. At one side, the answer is yes, it is the same God they worship because they both claim to worship the God of Adam, Noah, Abraham and Moses. On the other hand, a negative answer emerges because the idea of the God in this two religions are fundamentally different. Christians believe in Trinity, while Muslims do not.
Now, the question is, why the idea or concept of God is different? As both claim to worship God of Adam, Noah, Abraham and Moses, what was their concept of God? Is it possible that, the concept of God can be changed? Because, The God Himself claimed-"I do not change". Here comes Judaism. Because, they also claim to worship the same God, the God of those prophets. And Christians and Muslims agree that, upto a certain period, before the time of Jesus, this was the true religion of God. So, what is their concept of God? How do they see the concepts of God in the Christianity and Islam? And then I supplied a link to an from a sister SE site regarding the the opinion of Judaism about the concept of God in Islam.
Hope I am clear now.