All you have to do to see if Muslims worship the same God as Christians is to ask them who Jesus is. Jesus said:
11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
Jesus said that He and the Father are "one". That means Jesus is God, not the "prophet" of "Allah". If a Muslim denies the deity of Jesus, then he does not worship the Christian God.
It's as simple as that.
Qur'an 5:73 "They are surely disbelievers who blaspheme and say: God is one of three in the Trinity for there is no Ilah (God) except One, Allah. If they desist not from saying this (blasphemy), verily a grievous penalty will befall them - the disbelievers will suffer a painful doom."
Bible: The Antichrist is an unparalleled political, military and religious leader that will that emerge in the last-days.
Islam: The Mahdi is an unparalleled political, military and religious leader that will emerge in the last-days.
Bible: the False Prophet is a secondary prominent figure that will emerge in the last-days who will support the Antichrist.
Islam: the Muslim Jesus is a secondary prominent figure that will emerge in the last-days to support the Mahdi.
Bible: The Antichrist and the False Prophet together will have a powerful army that will do great damage to the earth in an effort to subdue every nation and dominate the World.
Islam: The Mahdi and the Muslim Jesus will have a powerful army that will attempt to control every nation of the earth and dominate the World.
Bible: The False Prophet is described essentially as a dragon in lambs clothing.
Islam: The Muslim Jesus literally comes bearing the name of the one that the world knows as The Lamb of God: Jesus Christ. Yet the Muslim Jesus comes to murder all those who do not submit to Islam.
Bible: The Antichrist and the False Prophet establish a New World Order.
Islam: The Mahdi and the Muslim Jesus establish a New World Order.
Bible: The Antichrist and the False Prophet institute new laws for the whole earth.
Islam: The Mahdi and the Muslim Jesus institute Islamic law all over the earth.
Bible: The Antichrist is said to change the times.
Islam: It is quite certain that if the Mahdi established Islam all over the earth, he would discontinue the use of Saturday and Sunday as the weekend or days of rest but rather Friday, the holy day of Islam. Also, he would most certainly eliminate the Gregorian calendar (A.D.), and replace it with the Islamic calendar (A. H.) as is used in every Islamic country.
Bible: The Antichrist and the False Prophet will both be powerful religious leaders who will attempt to institute a universal world religion.
Islam: The Mahdi and the Muslim Jesus will institute Islam as the only religion in the earth.
Bible: The Antichrist and the False Prophet will execute anyone who does not submit to their world religion.
Islam: Likewise, the Mahdi and the Muslim Jesus will execute anyone who does not submit to Islam.
Bible: The Antichrist and the False Prophet will specifically use beheading as the primary means of execution for non-conformists.
Islam: The Mahdi and the Muslim Jesus will use the Islamic practice of beheading for executions.
Bible: The Antichrist and the False Prophet will have a specific agenda to kill as many Jews as possible.
Islam: The Mahdi and the Muslim Jesus will kill as many Jews as is possible until only a few are left hiding behind rocks and trees.
Bible: The Antichrist and the False Prophet will attack to conquer and seize Jerusalem.
Islam: The Mahdi and the Muslim Jesus will attack to re-conquer and seize Jerusalem for Islam.
Bible: The Antichrist will set himself up in the Jewish temple as his seat of authority.
Islam: The Mahdi will establish the Islamic Caliphate from Jerusalem.
Bible: The False Prophet is said to do many miracles to deceive as many as possible into supporting the Antichrist.
Islam: The Mahdi himself is said to control the weather and the crops. His face is said to glow. We can also assume that since Jesus is viewed as having been empowered by Allah to work miracles when he was here on earth the first time, he will most likely be expected to continue to do so when he returns.
Bible: The Antichrist is described as riding on a white horse in the Book of Revelation
Islam: The Mahdi is described as riding on a white horse (ironically from the same verse).
Bible: The Antichrist is said to make a peace treaty with Israel for seven years.
Islam: The Mahdi is said to make a peace treaty through a Jew (specifically a Levite) for exactly seven years.
Bible: Jesus the Jewish Messiah will return to defend the Jews in Israel from a military attack from a vast coalition of nations led by the Antichrist and the False Prophet.
Islam: The Dajjal, the Islamic Antichrist will gain a great Jewish following and claim to be Jesus Christ and fight against the Mahdi and the Muslim Jesus.
Bible: The antichrist spirit specifically denies the most unique and central doctrines of Christianity, namely the trinity, the incarnation and the substitutionary death of Jesus on the cross.
Islam: Islam doctrinally and spiritually specifically denies the most unique and central doctrines of Christianity, namely the trinity, the incarnation and the substitutionary death of Jesus on the cross.
Bible: The primary warning of Jesus and the Apostle Paul was to warn Christians of the abundance of deceit and deception in the last-days.
Islam: Islam is perhaps the only religion in the earth that practices deceit as one of its tools to assist its own ascendancy. It actually has a specific doctrine which allows and even calls for deception to be used to achieve its desired end.
Bible: The specific nations pictured in the Bible as being part of the final empire of the Antichrist are all Islamic nations.
Islam: All Muslims are commanded to give their allegiance to The Mahdi as the final Caliph and Imam (leader) of Islam.
Bible: From the Bible and History we learn that the final Antichrist empire will be a revived version of the Empire that succeeds the Roman Empire
Islam: The Empire that succeeded the Roman/Byzantine Empire was the Islamic Ottoman Empire
Bible: When Antichrist emerges, there will already be some form of system in place that will be poised to receive him as a Savior and to give allegiance to him.
Islam: is already the second largest religion and will at present growth rates become the largest religion within a few decades. Islam is awaiting the coming of the Mahdi with a universal anticipation.