Back in 1994, I traveled to Israel to teach a programming class at an Intel facility in Haifa. The day before the class, I was hosted by a Christian Arab leader (not a Muslim convert) by arrangement with a University in the US. Prior to this, I had received a number of fascinating letters from the Jesus Film Project about this very phenomenon of Muslims becoming Christians due to a vision of Jesus.
After driving me all over Galilee, up into the Golan Heights and beyond that into a Druze village overlooking Mt. Hermon in Syria, he took me back to my hotel. A few nights later I visited his home to help him set up email. On the way back to Haifa that night, he told me a story about a newspaper account in the Haifa (Jewish) paper of a Muslim woman who had been admitted to a Jewish hospital in Haifa with cancer. According to the paper she reported having a vision of Jesus, was healed by Him and became a Christian. Note: I was blown away by this because I had not previously told him about the Jesus Film Project letters I had received.
My problem was that no Christian had been involved and I thought that God always uses believers to spread the Gospel.
When I got back to the states, my pastor (at that time) had me recount this story in all of the services one Sunday. Between two of the services, a person who was a missionary to the Philippines told me that there was a group of Christians there who were specifically praying that God would reveal Himself to Muslims in dreams because Muslims consider dreams to be authoritative. They also believe that demons cannot masquerade as prophets (e.g. Jesus) in dreams.
This appears to have been going on now for decades. Yes, many of these people are connecting up with Christian ministries (e.g. the Jesus Film Project, radio stations, etc.)
there was a group of Christians there who were specifically praying that God would reveal Himself to Muslims in dreams because Muslims consider dreams to be authoritative.
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I will start doing this.
Another consideration is the comment you made that the Muslims believe that demons cannot masquerade as prophets in dreams is that most consider that Satan does not see out thoughts as God does. Only God is omniscient.