Hmm. You may have hit a bug, I don't remember the letter (or journal can't remember which) having a specific name but after reading it the quest updated (or appeared in my case) in my journal along with a yellow search circle in the area. The quest merely said to search for the treasure in the area. I swam under the water in the area and found the chest and unlocked it.
I don't know what else to suggest, you've found the right body and he should have had the key and letter/journal on him. You should be able to unlock the chest. Have you got a recent save in the area to try again and see if reloading will cause the quest to work properly - that would be the other thing I would try.