Can he pray for his parents when he does not know what religion they were following when they died?

Praise be to Allah.

Since he comes from a kaafir nation, it is not permissible for him to pray for his parents, unless they had become Muslim, as Allaah says (interpretation of the meaning): 

“It is not (proper) for the Prophet and those who believe to ask Allaah’s forgiveness for the Mushrikoon, even though they be of kin, after it has become clear to them that they are the dwellers of the Fire (because they died in a state of disbelief).”

[al-Tawbah 9:113]