Pasban Mil Gaye Kaabe Ko Sanam Khane Se?

Re: Pasban Mil Gaye Kaabe Ko Sanam Khane Se?

That what the above clip also said that Mongols converted to Islam within 10 years after they conquered Muslim World. But I read that Baghdad was conquered by Hallaku (Grandson of Changez Khan), so this raise another question: Whether Hallaku converted to Islam before making all his plunder of a Muslim city Baghdad?