Praise be to Allah.
He is not allowed to do that, because this is cooperating in sin and transgression. He should not sign for the purpose of cremation. This is not acceptable according to sharee’ah. If the deceased is Muslim, it is not permissible to sign for his cremation. But if the deceased is a kaafir, then the matter is subject to further discussion, but to be on the safe side he should not sign, because it is not prescribed to cremate kaafirs. So to be on the safe side he should not sign. But if he is forced to do so, then the matter is easy with regard to a kaafir, but with regard to a Muslim, he should not sign. End quote.