This trap is the Dome of the Rock, one of the holiest sites in Islam, located precisely on the site of the Temple.

No, it's located on Fort Antonia, the only building the Romans didn't destroy when sacking Jerusalem. The wailing wall is fake. Christ prophesied and Roman historians confirmed that not one brick of the temple complex was left atop another. But the jews will destroy the dome and try to build a temple there anyway, and then things will get interesting as you said.

the prophecy made by the Islamic prophet Muhammad about the eschatological final solution

Who doesn't love eschatology, can you elaborate please? Also the temple was rebuilt- it was Jesus' resurrection. But I think you know that. Those who are perishing do not so here you go, guys:

"The Jews then responded to him, “What sign can you show us to prove your authority to do all this?Jesus answered them, “Destroy this temple, and in three days I will raise it up. They replied, “It has taken forty-six years to build this temple, and you are going to raise it in three days?” But the temple he had spoken of was his body." John 2:18-19