Those 13 years really took a toll on Professor X

The guys in the theatre behind me were chanting "3 DIDN'T HAPPEN" at the end of the newest movie. Seriously though, how did Xavier come back to life?

There was a post-credits scene were Xavier woke up in the body of a brain-dead patient, which was foreshadowed earlier in the movie when they were discussing hypothetical ethical cases such as "What if you could transfer someone's mind into the body of a brain-dead patient?" Not much mention of how he came to look and be disabled exactly like he was before. Edit: Apparently the credits imply that the patient was Xavier's identical twin.