I've been reading some articles and books about the early Islamic conquests that started at about 634 CE, mainly in areas that belonged to the Byzantine Empire. Problem is, the majority of works I've read until now emphasize the military or administrative aspects of these events, and when religion is mentioned it is only to explain discussions and polemics about Monophysites and Chalcedonians, making it seem that Islam didn't affect the empire at all. That can't be the case because, already in 656, Syria proclaimed Mu'awiya as a Caliph, starting a civil war that would end in 661 with his victory and the creation of the Umayyad Caliphate.¹
As I am very interested in contacts between different civilizations and how they affected common people, I am curious to know if there was some kind of major conversion to Islam in the conquered provinces of Syria, Egypt, Palestine, and others in the 7th century, or if that was a slow process.
¹The Cambridge History of the Byzantine Empire, pp. 230-231