Ok so you know that the nanosuit bonds to a persons neural network/mind along with his body, we learned this in Crysis 2 when Prophet said he had to die so it would change hosts, so he shot himself. However as the suit was progressively assimilating itself with Alcatraz in 2, something that took the entire game, it started to take a bit more personality. Notably, when Alcatraz was injured from destroying a Ceph tower and the suit said 'get your ass back in the game marine!'
Eventually at the end of the game the suit bonded 100% with Alcatraz but Prophets mind had imprinted itself in the suit, so even after he died it took on a 'Prophet' personality, and the two minds, Alcatraz and Nanosuit-Prophet, combined and became what is now Prophet. At the end of Crysis 2 when Rasch introduces himself he says 'Karl S. Rasch, at your service...and...you are?' and Alcatraz then says, 'They call me...Prophet.'
Basically the suit bonded with prophet and connected with his mind so much it left an imprint in the suit, which then imprinted to Alcatraz and Vulcan Mind Melded the two together.