Reference: Fataawa al-Lajnah ad-Daa.imah lil-Buhooth al-‘Ilmiyyah wal-Iftaa., – Volume 9, Page 10, Question 3 of Fatwa No.5124
Question: Is it permissible to bury a non-Muslim child in a Muslim graveyard if a Muslim has adopted him, and then he (the child) dies before reaching the age of puberty?
Response: It is not permissible to bury a non-Muslim in a Muslim graveyard, regardless of whether he was adopted by a Muslim or not, or whether he had reached the age of puberty or not. However, if there was any indication as to his [having embraced] Islaam, then he is to be buried in a Muslim graveyard. It should be noted that adoption is forbidden in Islaam [while fostering is permissible], because Allaah (Subhaanahu wa Ta’aala) says:
{Call them (adopted sons) by [the names of] their fathers}, [Soorah al-Ahzaab, Aayah 5].
And with Allaah lies all success and may Allaah send prayers and salutations upon our Prophet ﷺ and his family and his companions.