This part of the Soluce Fallout 4 : Far Harbor is dedicated to the Faction quest "The Heretic". Richter asks you to find a former member of the cult who has gone completely insane.
Acquired: Grand Devotee Richter
Condition: Complete the quest "Visions in the Fog"
Reward: 508Xp + Atom Judgment
Associated Quest: “What Atom Wants”
At the Core, talk to Richter and offer him your help to receive this mission (picture1). At the end of the dialogue, go to the devout Theil and ask her about Gwyneth (picture2).
Once this operation is completed, you will have to go to the two holy places indicated on your map in order to recover the impious graffiti (picture3). When you have succeeded, go to the new objective marker and search the back house to retrieve a recording (pictures4-5).
After listening to it, head towards the old church to find Gwyneth, you then have several choices (picture6). You can kill her without warning, convince her to return to the Children of Atom or to leave the island for good (picture7). In any case, you can then return to Richter to complete the quest and receive your reward (picture8).