I've had a similar thing occur but it seems to be random where it'll sometimes show and not show. At first the carpenter gear I had crafted wasn't showing who made it. But on another log it it showed it again.

Also this might be related to the fact you traded the item but I know with Mog Mail when you send an item through the mail it won't show the materia that is on the weapon until you pull it out so it could be the same occurrence with the item.

Other thing to notice is the picture provided does show a blank space under the Sells for part which means that the item is still "signed" but not visible. You may want to try logging in and out to see if the gear shows up signed for them after they relog.