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Background
You'll trigger this task when you inspect the hanged man (#1) and notice that he's only wearing boots.
Walkthrough
If you ask Cuno (#2) about the missing armor, then he'll tell you two things of interest: that he threw the helmet into the sea, and that Call-Me-Manana (#3) was snooping around the corpse. When you talk to Manana, he'll admit to investigating the "armor situation" for the Dockworkers' Union, and he'll reveal that there are four pieces to the set. But he'll claim that he didn't take any of them, and that Cuno is just trying to cause trouble.
At this point, you'll have to make a decision: to track down the entire armor set or just one piece of it. This will trigger the task
Find All Armour Pieces or
Find One Armour Piece (the latter is easier to complete but the former is worth more xp). If you haven't yet triggered the task
Getting the Hanged Man's Boots, then you'll trigger that as well.
When you return to Cuno, if you have Suggestion 5, then you'll be able to thank him for the tip. This will make him look like a snitch, which will give you a +2 bonus when trying to pass the Empathy check with him later (see Cuno's entry in the
Martinaise East page for details). But regardless, talking to Cuno will complete the task and earn you 10 xp.
1 - Hanged Man
2 - Cuno
3 - Call-Me-Manana