If your characters are on different servers, you can't share items between them. Only characters on the same server and in the same city on the same account can share items between each other that are not "No Drop" flagged. Items that are attunable but not yet attuned can be placed in the shared bank slots. Lore items cannot be placed in the shared slot.
As for moving your characters to the same server, that's not possible at this time unless specifically part of a server move initiated by Sony and often that would be from a crowed server to one less crowded and those applying for the move, are not actually gauranteed that they will be moved, and have no choice as to the server they are moving to, although Sony often publicizes to which server the move is being made to.
In summary, you are out of luck with those two characters ever sharing anything with each other. I would suggest starting another character on the same server as the one you wish to exchange items from. You can select which server you wish to create a character on during the character creation process, even on servers marked as "full".