Hadithcore
Mishkat al-Masabih, 4067

He reported God’s messenger as saying, “When you shoot your arrow and the animal goes out of your sight, eat it when you come upon it, provided it has not a stench.” (Bukhari and Muslim.)

وَعَنْهُ قَالَ: قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ: «إِذَا رَمَيْتَ بِسَهْمِكَ فَغَابَ عَنْكَ فَأَدْرَكْتَهُ فَكُلْ مَا لَمْ يُنْتِنْ» . رَوَاهُ مُسْلِمٌ

References1 variant
In-Book Reference
Book 20, Hadith 4