Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: The Prophet (peace and blessings be upon him) said: "When you send your dog and it eats from the game, do not eat that game, for it must have caught it for itself; and when you send it and it kills the game without eating from it, then eat that game, for it must have caught it for its master."
Ahmad recorded it, and its narrators are the narrators of the Sahih.