A Loose End

A Loose End is a Brotherhood of Steel side quest in Fallout 4.

Quick walkthrough
Liberty Reprimed does not need to be completed to start this quest, one needs only to finish the 'Speak to Doctor Li' objective. Captain Kells wants you to kill Virgil. Alternatively you can convince Kells with a speech check that Virgil has been cured and is no longer a threat.

Detailed walkthrough
The quest begins when the Sole Survivor speaks with Lancer Captain Kells. He informs the player that the Super Mutant 'Virgil' must be killed, the Sole Survivor then must talk to Virgil. The player will then have the choice to either kill Virgil or spare him and lie to Captain Kells. After picking either option the player must report back to Captain Kells who will reward the Sole Survivor with the Visionary's T-60c helmet.