No, the Doctor cannot save Moriarty with the Tardis. He blew his brains out with a very big gun. Accept it.

Sorry andrew Scott and Moriarty fans (and I’m one as well), but the best we can hope for is his reappearance as a flashback. That was a very large gun which would have made a huge hole in Moriarty’s head (really, be thankful they didn’t decide to be graphically accurate). Moriarty wouldn’t have had enough brains left to read Hello.