Moriarty came to his lover's apartment in the evening and saw that he had been killed, he took the cartridges and bullets to conduct his own investigation. After investigating, he brutally killed those bandits and came to Sherlock so that Sherlock kill him because Moriarty had no reason to live. His beloved is killed, and his interest in confronting Sherlock has disappeared, so he wants Sherlock to die, and for this he brought a gun. He doesn't know anything about your investigation.