This is given by the High Confessor Tektus after talking to him the first time and offering your help for the cult, during the checklist quest “What Atom Requires”. Read the note he gave you to find the name of the person you should investigate.
In the vessel, search for a note in Sister Aubert’s bunk. The note should be tucked in under the bed. Leave the sub then get the hidden footlocker keys behind the bench in the locker room, past the decontamination arch. Return back to the sub and follow the quest markers to find Aubert and Edgar’s footlocker. Get the note inside and read it. Once done, you can either report to the High Confessor immediately or talk to Sister Aubert first.
If you talk to Aubert first, she’ll beg you to hand her the note you found. You can give it to her or tell her to escape before you talk with the high confessor. You can also lie about Aubert’s loyalty through a successful speech check. After choosing the resolution you want, the quest will be complete and you’ll receive the Inquisitor’s Cowl.