Sims 3 - Island Paradise: Reconstructing the uncharted island map?

Okay. My two Sims each have two map pieces, so I have all four, but it won't let me reconstruct the map because I can't take two map pieces out of one of my Sims' inventory and give them to my other Sim. It wont let me give it as a gift, it wont let me put it on the floor so my other Sim can collect it.

I have all of the map pieces, the game wont let me reconstruct it because the pieces are separated between my Sims.

How do I reconstruct the map?