Ibn Abi al-Zinad (may Allah have mercy on him) narrates from his father (may Allah have mercy on him), from the reliable jurists, that game killed by a trained dog or falcon is lawful, even if the dog or falcon eats from that game.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18886