I can't remember if this was ever spelled out in the books, but why does drinking from the Mortal Cup give Simon back his memories?

I can't remember if this was ever spelled out in the books, but why does drinking from the Mortal Cup give Simon back his memories? It seemed to me that it was just taken for granted that it would help, but why? What power does the Mortal Cup have to give back memories taken away by a demon?