The Muslim Jesus cannot be the New Testament Jesus because, according to Muslims, the New Testament is corrupt. They may say to Christians we share your values, but among themselves they view Christians as delusional for believing in Jesus Christ:

Planck's Constant, Is the Quran Based on the Bible?

... to the People of the Book (as Jews and Christians are called), Islam is presented as just another Abrahamic faith that shares their common values and spiritual traditions and that recognizes their Holy Books. Among themselves, Muslims see the People of the Book as poor deluded souls who believe in vile, corrupt, miscreant and unholy texts and who must, in the end, be either persuaded to see things the Muslim way or be subjugate and pay a tax.

As to why Muslims say that the Christian and Jewish Holy Books are corrupt - the answer is simple: because those books do not mention Mohammed. Muslims always tell infidels that they believe in the four books of God: The Torah, The Psalms, The Gospels, and The Holy Quran. But when one asks Muslims why none of the first three Holy Books ever mention Mohammed as the final Prophet of God, they use as excuse, that Christians and Jews have excised all references to Mohammed, thus corrupting those books.

Planck's Constant, Do Muslims Believe anything in the Bible?

If the Torah and the Gospels contain the original, untarnished, uncorrupted texts of the Holy Word of God, why would we even need the Quran? No, dear infidel, when Muslims say they respect Jews and Christians because we are "people of the book," it is nothing but a lie to lower our guard, to make us think that Islam is a real religion instead of the fraud it really is. When Muslims read passages in the Quran that are supposedly from "the Bible" they are reading words that do not exist in either the Torah or the Gospels. Muslims believe in only the parts of the Bible that agree with the Quran. The parts that contradict the Quran are not the Truth.

The next time a Muslim tells you that he believes in the same Jesus as Christians, ask if Jesus, the one in the Quran, was crucified. If he tells the truth, he will admit that no, the Jesus in the Quran was never crucified, in fact was not killed at all but raised to Heaven by Allah. Then just to have fun with him, ask if the Jews were responsible for Christ's Death. Here we will have an interesting contradiction. Despite the fact that the Quran categorically states that the Jews did not kill Jesus, most Muslims will still tell you that the Jews killed Jesus Christ. They will say this of course, because they hate Jews and blame them for everything, see my article 13 things to blame on the Jews.

The photo of the Muslim Jesus is from the Dec 10 2009 Issue of the New Statesman:

Jesus: the Muslim prophet

Christians, perhaps because they call themselves Christians and believe in Christianity, like to claim ownership of Christ. But the veneration of Jesus by Muslims began during the lifetime of the Prophet of Islam. Perhaps most telling is the story in the classical biographies of Muhammad, who, entering the city of Mecca in triumph in 630AD, proceeded at once to the Kaaba to cleanse the holy shrine of its idols. As he walked around, ordering the destruction of the pictures and statues of the 360 or so pagan deities, he came across a fresco on the wall depicting the Virgin and Child. He is said to have covered it reverently with his cloak and decreed that all other paintings be washed away except that one.

Jesus, or Isa, as he is known in Arabic, is deemed by Islam to be a Muslim prophet rather than the Son of God, or God incarnate. He is referred to by name in as many as 25 different verses of the Quran and six times with the title of "Messiah" (or "Christ", depending on which Quranic translation is being used). He is also referred to as the "Messenger" and the "Prophet" but, perhaps above all else, as the "Word" and the "Spirit" of God. No other prophet in the Quran, not even Muhammad, is given this particular honour. In fact, among the 124,000 prophets said to be recognised by Islam - a figure that includes all of the Jewish prophets of the Old Testament - Jesus is considered second only to Muhammad, and is believed to be the precursor to the Prophet of Islam.

In this Youtube video, we can see the Muslim lie that they believe in the same Jesus as Christians.

Notes

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The Guardian, TV airing for Islam's story of Christ

There was no manger, Christ is not the Messiah, and the crucifixion never happened. A forthcoming ITV documentary will portray Jesus as Muslims see him.

With the Koran as a main source and drawing on interviews with scholars and historians, the Muslim Jesus explores how Islam honours Christ as a prophet but not as the son of God. According to the Koran the crucifixion was a divine illusion. Instead of dying on the cross, Jesus was rescued by angels and raised to heaven.