They believe that but it is a lie. Jerusalem is not even mentioned in The Unholy Koran.
The place of the 'ascension' (that word should give you a clue to the true nature of "The Prophet" of Islam) is said to have been at place called "The farthest mosque". It's a chapter in The Koran called The Night Journey.
At the time this verse was "revealed" [about 622AD] Jerusalem was not in the hands of Muslims and there was no Mosque at all in this place (not even a church). The Dome of the Rock and the Al Aqsa Mosque only began to be built 53 years after the death of the false prophet Muhammad.
Very enlightening.