It seems a lot of viewers believe that Moriarty was "programmed" by Eurus to make trouble for Sherlock. But this doesn't really add up.
First of all, we know that Moriarty knew about Sherlock in 2010, the time of The Great Game. It seems quite likely that he probably knew about Sherlock as far back as when Carl Powers was murdered by JM and Sherlock was the only one who knew Carl's death wasn't an accident, but couldn't get anyone to listen to him.
Second, the meeting between Moriarty and Eurus happened "five years ago", so either in 2012 or 2011, which places it chronologically after The Great Game.
Of course it would have been prior to The Reichenbach Fall but even still, the Moriarty/Eurus connection could only have been a "collaboration" at best. After all, JM was a psychopath from birth. He didn't need anyone to "program him" to go after Sherlock.