Have to be a member of faction(and rank 10, i think it was, unless they changed that), and both people have to be inside the fief.
You should not be required to have someone join your faction to make the transfer. I would never let someone in another faction have the ability to see the position, direction, and equipment of other clan members; that's a huge security liability. (I just checked, and rank 1 faction members can see all of this information.)
If you're worried about people accidentally clicking on the wrong name for the transfer, add an "Are you sure?" dialog, or require password entry like everywhere else on the website.
Can anyone verify that you can only transfer a fief to someone in your faction? You can set a member to rank 0 to kick them out temporarily, and their line in the table will automatically turn into an application with an "Accept"/"Reject" input.
While you're at it, if you find that they must be in the faction, find out what the rank must be to receive a fief, and what rank is required to give it back, because these are all important (and undocumented) numbers.