With This Ring... is a side quest in Prey (2017).
You can pull up Nicole Hague’s tracking bracelet on any security station computer, or you can read the next sentence. She’s in the Executive Suites area of the Crew Quarters. You’ll need the Executive Suites grav lift keycode to get up there. You can find it in the supply closet on the second floor to the left of the Yellow Tulip. (This is the same closet where you investigate Captain Stabfellow’s map in "Treasure Hunt.")
The first time you enter the Executive Suites, you’ll encounter Nicole in her phantom form. She’s in the Guest Suite at the end of the hall along with the phantom of Argenteno Pero. Shoot her and loot her corpse for a neuromod, a recycler charge and the wedding ring.
Return the ring to Kevin who will be vaguely upset to learn what happened to his wife. At this point the quest will complete.