Return to Acadia, and search the lab terminal on the northern end of the lowest level. In the past projects listed are note on "reconstruction surgery 009" which concerns Victoria's (now Jule's) surgery.
From here, there are two options: tell Cog about Jule's past and keep it secret from her, or tell Jule's about her past.
Telling Cog about Jule's past will ensure that Jule doesn't know what happened to her and gives her a chance at happiness.
Telling Jule about her past will result in her becoming furious with her "friends" deciding to save Victoria and therefore destroy what made her her. She will abandon Acadia and give the Sole Survivor the key to a lock box in the basement holding all of her possessions.
Speak with Jule
Cog is concerned about Jule's mental state, and has asked that I speak with her.
Speak to Cog
At Cog's insistence, Jule has told me about some things she can't quite remember, and has given me a key she thinks is important. I should talk to Cog about what all this means.
Investigate the Boat
Cog is concerned about Jule's mental state; he believes that there's some connection to the boat Faraday sent me to and things Jule can't quite remember. I should return to the boat with the key I was given, and see what I can find.
Search the Lab Terminal
Cog has suspicions about Jule's mental state, and asked me to look into the matter. On a wrecked boat on the island, I've found a note referencing Faraday's lab terminal - I should find out if it's connected.
Tell Cog about Jule's past
After being asked to look into something that may have happened to Jule, I've learned that she used to be a synth named Victoria. After an accident, she had her mind wiped without her knowledge. Now I need to decide what to do with this information.
Tell Jule about her past
Cog had suspicions about something that happened to Jule; it turns out her mind was wiped without her knowledge, leaving her in a very affected state. I've resolved the issue as best I can.
Banner piece ·Buried stash ·Campground banner ·Heretical sign ·Islander's Almanac ·Missing synth's head ·Remains of Pepper ·Remains of Pepper II ·Remains of Mr. Purrs ·Remain of Sir Cattington ·Remains of Missy I ·Remains of Missy II ·Remains of Missy IV ·Storage drive