Very well. Without paying any attention to what anyone does or does not believe, yes, everything that @anon61221983 and @chenille have said is true and correct. Judaism, Christianity and Islam do in fact worship the same god, and this is backed by scripture and thousands of years of history. The theological underpinnings of all three religions sprang from the God of Abraham, and although the religions themselves have gone down separate theological paths, the central god is still shared in common between them as a fundamental pillar of faith among all three. The vast majority of Muslims knowingly worship the same god as Christians, and this has been the case throughout history, where Jews and Christians were given special privileges not afforded to Pagans within Muslim societies as People of the Book.
There are currently some ignorant Christians and ignorant Muslims who reject all of the above, but that is a matter of belief and so beyond the scope of this conversation. I apologize for wading into the murky waters of personal beliefs in a conversation about the facts of the Abrahamic Faiths. I was trying to take a sociological approach to a theological debate, and that only led to confusion. I did not mean to say that facts are wrong or unimportant; I merely wanted to say that we should not simply ignore personal beliefs, especially when they lead to conflict. I did not intend to propagate any of these beliefs.
If we are sticking strictly to facts, then there is really nothing else to argue because the facts laid out by @anon61221983 and @chenille are undeniable facts about the three Abrahamic Faiths. Modern tensions between Jews, Christians and Muslims are largely artificial and based on more recently added mutual misconceptions, of which the idea that they believe in different gods is one unfortunate example.
Whether and to what extent Muslims and Christians actually believe these misconceptions is beyond the scope of this conversation, but it is unfortunate that these beliefs are still propagated among both communities.
In the future, I will try not to draw attention to these beliefs (even in the context of explaining how a single religion can have a spectrum of contradictory beliefs) because, as @anon61221983 said, these believes have been leading to enormous loss of life.
As for what people actually believe in their heart of hearts, I will try not to speculate.
As for Judaism, Islam and Christianity, I think that they are all really beautiful religions that have brought many wonderful and meaningful things to humanity, and it breaks my heart to see conflict between them in spite of their many core similarities.