The vast majority of Syrian refugees are going to try their best to stay in Europe because why would they want to leave to return to devastation and ruin (aside from forced deportation).
The asylum claim processing authorities were a bit overwhelmed, but soon learned to ask questions such as "can you tell me in which city you used to live, what was the name of the mayor, what was the closest mosque/church, your address, your school" etc. Few of the fake ones could answer such probing in a satisfying way.