The Price of Memory

The Price of Memory is a side quest $$==Quick walkthrough==

Detailed walkthrough
After speaking with Jule and completing the quest Data Recovery, speaking with Cog will lead to him taking the Sole Survivor to see Jule about her problems. After some convincing, Jule will speak with the Survivor and hand them Victoria's key, indicating that the wrecked tugboat near the flames at the Southwest Harbor has something to do with her memories. The key will unlock the steamer trunk on the aft end of the tugboat, allowing Victoria's note to be collected from the trunk. The note indicates something is hidden on Faraday's terminal at Acadia and reading the Reconstruction Surgery 009 entry under Past Projects on the terminal reveals more information about Jule.

From here, the Sole Survivor may either relay the information to Cog and agree to keep it a secret or tell Jule about her past. Siding with Cog completes the quest and he will give the Sole Survivor a crippling sledgehammer as a reward.

Completing the quest by telling Jule about herself will get the player character Jule's key which can be used to unlock Jule's chest. The chest is located down the north stairwell in the extended alcove left of the stairwell exit. It is on the bottom of the shelves at the back of the extended alcove. It contains the unyielding synth chest piece, the only guaranteed piece of 'unyielding' armor.