Yeah, you see. The winner and the one the winner selects (in your case, Shawk1), gets rights to pass rights (Complicated, hum?) I'll show you an example I've posted on the giveaway thread:
Z is a Winner
X gets Lugia from Z, X can redis the poke.
Y gets Lugia from X, Y cannot redis.
In your case, Shawk would also be a Z, and Dragon FE would be a X.