This question is even harder to answer than the question addressed in the previous post whether Christians and Muslims worship the same God. Christianity is sometimes spoken of as a daughter religion of Judaism. It is more accurate to speak of them as siblings. Both have the Hebrew Bible / Old Testament as their first canonical document. Both have arguably been shaped as much or more by a second volume, the New Testament in one case, the Talmud in the other. Events in the first century were obviously crucial for the development of the Christian faith; the destruction of the temple within a generation of the life, death and resurrection of Jesus was arguably just as decisive for Judaism.
But this is not the chief obstacle in addressing the question of the title. The chief obstacle is that being Jewish is an ethnic and cultural identity at least as much as a religious one. Many Jews are agnostics or atheists. A good few Jews are Christians. Some Jews dabble in New Age spiritualities, others follow one of a number of ultra-orthodox traditions. There are orthodox, conservative and liberal interpretations of Jewish faith and traditions.
In other words, it is perfectly impossible to generalise about Jewish theology. Christianity and Islam have of course their own divisions and denominations but what they are agreed on arguably provides a sufficient core for at least addressing the question whether Christians and Muslims worship the same God.
I see no benefit in developing a detailed taxonomy but maybe four things can be said by way of a rough sketch of some configurations.
(1) Jewish atheists do not worship the same God as Christians.
(2) Jewish Christians worship the same God as non-Jewish Christians.
(3) The concept of God held by many Jews is probably less definitive than that held by most Muslims. For Muslims the Quran offers an authoritative account of God which is explicitly formulated over against the Christian faith. With a less definitive picture it becomes harder to say whether an account is an inadequate portrayal of God or an account of a different “God”.
(4) Forms of Jewish belief in which the Hebrew Bible is read through the lens of a more definitive theology which has been developed in monistic or other anti-Christian ways are closer to presenting an account of a fictional character based on a real person (as I have suggested for Islam) than forms of Jewish belief which are open to a variety of experiences and descriptions of God.
And two final points, not so much by way of conclusion but as a reminder:
(5) There is a significant difference between a (Jewish) prayer whose words a Christian can appropriate without qualms and a (Muslim) prayer which makes claims that a Christian cannot affirm.
(6) A Christian prays in the name of Christ and by the power of the Holy Spirit to the Father or to Jesus or to the Holy Spirit.
 It is not generally considered possible for a Muslim or Christian to be an atheist and rightly so. An atheist can emerge from a Muslim or Christian background but they cease to be Christian or Muslim (in anything but maybe the vaguest cultural sense) when they identify as atheists. A Jewish atheist does not cease to be a Jew.
 The Christian faith is misrepresented in the Quran but this misrepresentation is canonical and there is no ground for believing that a properly understood Trinitarian faith would be acceptable to any school of Islamic theology.
 The same question arises with regard to other, modern movements. Mormonism may be closer to misrepresenting the true God, while Deism present a different “God” from Christianity.