Jami` at-Tirmidhi Book 18, Hadith 6
"I said: 'O Messenger of Allah! I shoot some game and then find my arrow in it the next day.' He said: 'If you know that your arrow killed it, and you dont see any marks of predators, then eat it.'"
"I asked the Messenger of Allah (ﷺ) about the game caught by a falcon. So he said: 'What it catches for you, then eat it.'"
"I asked the Messenger of Allah (ﷺ) about hunting, so he said: 'Mention Allah's Name when you shoot your arrow. Then, if you find it dead, eat from it, unless you found that it has fallen in (some body of) water. Then do not eat it, for you do not know if the water killed it, or your arrow.'"