This quest will begin immediately after you find out the real murderer. You have the option to tell the results of your investigation to Maxwell and if you agreed to let Ezra go, you can reveal the truth to Maxwell as well to make the Vault's security attack Ezra. Ezra will attempt to escape. When he does, it's safe to attack him and destroy him. You can loot his body for the key and more caps. Finally, talk to Maxwell to complete both quests.