Ah, but you're assuming that a Muslim interprets his religion in a way that causes him to believe in souls and a creator God. For instance, I believe in the soul and in God, but that's because I recognise them as correlates of experience; therefore I suppose I don't really believe, but know.
As to how I define these things in a Buddhist sense: the soul is nibbana. Nibbana is dwelling in God's presence.
Essentially, there is nothing but nibbana, only beginningless ignorance, not itself an element, not itself real, keeps us in samsara. Don't ask me to speculate on the beginnings of ignorance (something I've spent fruitless hours wondering about in the past): the Buddha himself explained:
"Suppose a man is struck by a poisoned arrow and the doctor wishes to take out the arrow immediately. Suppose the man does not want the arrow removed until he knows who shot it, his age, his parents, and why he shot it. What would happen? If he were to wait until all these questions have been answered, the man might die first."
(from the Arrow Sutra)
p.s. Jihad is the practice of ending ignorance. I think the Muslim faith contains much that is beautiful, by the way, though like other faiths, not everyone who practices it is the best example of said beauty. As-Salāmu `Alaykum