This trick will allow you to clone a monster to give to a friend's game/save file, while keeping the original monster.

#1. Make sure you are in the town area and your current character has the "Moon Lighter" or "Moon Lighter S" item with him/her.
#2. Save your game at Sword's House and walk to the VMU machine in the Monster House.
#3. Download the "Moon Lighter" or "Moon Lighter S" mini-game onto your VMU.
#4. Download the monster you wish to clone onto the VMU.
#5. After it has finished downloading, exit the Monster House. WITHOUT SAVING, turn the game off.
#6. Turn the game on and select your friend's save file. Go to the Monster House and load the monster from the VMU into the game. If done correctly, both save files should have a copy of the same monster!