Short answer: Possibly, but it's complicated.
My view: It's hard to answer that Jews, Christians and Muslims worship the same God or not because everyone claim that they have the Truth. Even I myself will firmly say that what I believe is the Truth(Christianity). The deeper we go inside any of these religion, the bigger their differences are.
Our source is the same: We all sprang from one root and there are many branches, more will come as time passes. First, there was only the Jewish religion. Secondly, Christianity sprang up from Judaism and the Third is Islam. Now, Mormons, Bahai and so on....
More branches will keep on coming.
It is up to the individuals to decide what is the true religion. As for myself, after studying all major religions, I found satisfaction in Christianity with strong believe in the Trinity.
My personal belief: Judaism is the parent religion for any Abrahamic religions and it deserves respect from all. Where would we all be if Judaism was not there? I do not like it when the Qura'n makes insults about Judaism. Christianity is the completion or final stage of Abrahamic religion. Islam is a heresy created by borrowing the concepts from Judaism and Christianity. (This is only my personal belief and please don't take it seriously or personally. Thanks)
My answer: Christian God is exactly the same as the Jewish God. Christians simply see Him as a God with three personalities and that He sent His Son as the Messiah to die for our sins. What ever the Jews believed before the birth of Jesus Christ is also the same belief for the Christians. The Scripture of the Jews contains prophecies about the Messiah to come. The New Testament confirms with many evidence that Jesus Christ is the Messiah promised by the Jewish Scripture. The Jews are still waiting for the Messiah to come.
The New Testament gives a more detail picture of who the Messiah is.
Matthew 22:41-46 (NIV)
While the Pharisees were gathered together, Jesus asked them, “What do you think about the Messiah? Whose son is he?”
“The son of David,” they replied.
He said to them, “How is it then that David, speaking by the
Spirit, calls him ‘Lord’? For he says,
“‘The Lord said to my Lord: “Sit at my right hand until I put your enemies under your feet.”’ (Psalm 110)
If then David calls him ‘Lord,’ how can he be his son?” No one could say a word in reply, and from that day on no one dared to ask him any more questions.
Jesus Christ is the Word of God, the promised Messiah who was with God from the beginning and born as man without sin to die for our sins.
John 1:14 (NIV) The Word became flesh and made his dwelling among us.
We have seen his glory, the glory of the one and only Son, who came
from the Father, full of grace and truth.