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Grapsus tenuicrustatus
Spotted off a pier in Key West, Florida.
It's not a Mangrove Tree Crab. Unfortunately I don't think it is native. I'm not really sure, but I found this online http://dusttracks.com/2011/07/05/the-sal.... It's a very similar picture to yours in Key West too. On this blog it said it might be a Thin-shelled Rock Crab (Grapsus tenuicrustatus). This is a very excellent spotting!