The ship stern is on the aft (rear) part of the Upper Deck of the The Providence.
You go there after talking to James to Look for clues
Dialog[edit]
Sailor: Evening, sir.
Haytham Kenway: How are things?
Sailor: Calm and quiet. Just the way I like it. What brings you topside?
Haytham: Thought I'd wander a bit. Stretch my legs. That's all.
Sailor: Take care where you tread. The deck hides all manner of danger in the dark.
(Splashing noise sounds)
Haytham: What was that? ... Someone's throwing cargo overboard... but why?