I have 2 current theories on how Moriarty survived.
1. He used a real gun, but the chamber was empty. Moriarty had snipers, right? He could've had one of them fire a shot, near Moriarty. Also, as Moriarty had a coat with a collar, he could've had a blood pouch hidden, and it exploded as he fell. Notice how the blood didn't splatter, but it just streamed when he fell. Also, how could he have kept hold of the gun?
2. Moriarty and Sherlock both knew they were going to fake their suicides. Who knows if they've spoken to each other off screen? The thing is about Sherlock and Moriarty is they're rivals. They're two geniuses playing a game of chess. Moriarty could've made a deal with Sherlock that if his suicide was more convincing than Sherlock's, then he wouldn't reveal the full extent of his network. But if Sherlock did, then Moriarty would let him dismantle it.
Problems:
The second theory sounds quite dumb, but knowing the writers, anything is possible.
Support:
I don't think Richard Brook is real, because the man on that roof acted too much like Moriarty to be someone else. Also, Moriarty is just as smart as Sherlock, so he'd know if Sherlock was going to fake his death. Also, Moriarty most likely predicted that Sherlock had a plan due to the fact that Sherlock set up the meeting place. And Sherlock's fake suicide wouldn't have worked if Moriarty was still alive, because Moriarty would've looked down to make sure he died. Also, Mycroft didn't release the GIF so Sherlock could come back because Mycroft would be in so much trouble with the government. Despite the fact that Moriarty "is" the British government, how come he couldn't stop Sherlock being exiled? And even the Prime Minister was notified, so he'd be in a lot of trouble. And where did Mycroft get the footage? Also, I don't think it's another villain because why would they want SHERLOCK HOLMES, the world's greatest detective, to come and foil their plan? In addition, I don't think it was Moriarty's Network, because Sherlock dismantled it. Even if he didn't, they probably wouldn't want Sherlock to return either. Also, Andrew Scott even confirmed that the writers had planned his return from the Reicanbach Fall, so all Sherlockians should start watching to see how he did it. I do think Moriarty is truly back, because during each season, one of the three episodes have been based on a novel. The three novels that have been used are A Study in Scarlet (A Study in Pink S1 E1), The Hound of the Baskerville (The Hounds of Baskerville S2 E2), and The Sign of Four (The Sign of Three S3 E2). There is one Sherlock Holmes Novel left: The Valley of Fear, which introudced Moriarty as a villain. This novel may be based off of for an episode for Season 4. This adds to the evidence that Moriarty is back and kicking. #MoriartyLives