Witch Hunt

Witch Hunt is a side quest in the Fallout 4 add-on Far Harbor.

Quick walkthrough
The High Confessor give you the task to look into one of his "loyal" subjects, Aubert. Find her and talk to her. Once the conversation has started she reveals that she doesn't believe in the High Confessor. You then search her bunk and find a note between her and someone else. To complete the quest choose to either turn Aubert in to the High Confessor, or to spare Aubert and try to lie to the High Confessor. If the High Confessor believes you or you turn Aubert in you are rewarded with the Inquisitor's cowl unique helm.

Detailed walkthrough
This quest is provided as part of the optional objective "Help the High Confessor" under What Atom Requires. Asking him if there's any work to be done will result in him demanding the player investigate a member of the cult for disloyalty, handing over the High Confessor's note. Reading the note reveals this person as Sister Aubert, at which point Edgar's note becomes available tucked under her bunk in the Vessel. Reading this note leads to the Footlocker key near the entrance to the Nucleus, which opens Edgar and Aubert's footlocker back on the Vessel. Inside is Aubert's note, which denounces the High Confessor and accuses him of having Edgar killed.

At this point the player can either bring the note directly to the High Confessor, thus concluding the quest, receiving the Inquisitor's cowl, and presumably getting Aubert killed for her disloyalty, or they can confront Aubert. If the latter option is taken, she will beg for the note to be handed over so she can destroy it. The player can tell her to run, ask for payment (about 95 caps), hand the note over, or withhold the decision.

When talking to the High Confessor, the player has to option to lie (medium Charisma check) that Aubert is loyal, thus receiving the Inquisitor's cowl without condemning her. If the check fails and the note was given back to her, the only option is to lie and say that no proof was found. The High Confessor is disappointed with this result and keeps the cowl, but the quest concludes.