Hey there, if you've completed it on one character I don't think you can progress it on others.
I know Cryptic Quatrains I and II say 'Treasure already discovered, this can be safely dismantled'.
Edit: People will just randomly downvote everything, no one should take it personally.
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I agree with what your saying. I got the 3rd treasure map on my Hunter and ran out of time that day to do it. I then picked it up and completed it with my Titan. My Hunter still has the map and I completed it a second time just to get it out of my inventory. The treasure chest isn't there because I claimed it. The bad part is that even though I "abandoned" the treasure map, it still shows up in Helm Abandoned quest list and can't be removed. Sort of annoying.
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THANKS!