Have a pre-hunt get together and let everyone know there are going to be some expectations that must be complied with. Let the group know every bird taken will be dressed by the person who shot it. Tell the group a couple people have raised a concern about birds being left for others to clean. Ask for a show of hands as to all those in agreement. Address any concerns about cleaning and restate the policy. By addressing the group in a manner like this you aren't singling him out and it gives him a chance to save face and friendships.

"One of our group (shoots a Parker) will neither clean nor consume his own birds . He'll empty his bag into the communal pile and retire to the shade to check his phone messages and wait for lunch."

A different take: You only have one not pulling his load. To bring this up in a group will ruffle the feathers of one or more of those who do their part plus the dead weight hunter. Better to get him beforehand or off to the side and tell him what you and everyone expects. Then if he gets mad, he was not a friend. If he then joins in no one will be the wiser what happened. He probably does not know it is irritating everyone. My 2 cents.