Here's the sequence.
1. Open a mail and start writing to Player A
2. Player B starts trade with you.
3. During the trade, send the mail to Player A to close the mail dialog box. (Not sure if I populated the trade box before or after sending the mail).
4. Complete trade with Character B per usual.
Result: I was trading two Humbaba emblems for two other emblems. It looked like a legit trade, but upon completion one of the Humbabas was sent to Player A and Player B received only one emblem. I received both emblems of the trade from Player B.
P.S. In this case, I gave Player B another Humbaba, trusting they didn't receive it. Player A later told me they received a Humbaba and returned it. So, good example of how trustworthy most people are in the game. But, I still thought it worth reporting.