All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
All that a Muslim is allowed to do for a dead non-Muslim is bury him if there are no non-Muslims to do this task. However, digging the grave and erecting a cross grave marker over it is prohibited for a number of reasons:
* The cross is a slogan of the non-Muslims and a sign of lying, deviation and idolatry.
* The cross is an idol and the Prophet, sallallaahu ‘alayhi wa sallam, commanded us to destroy idols. It was narrated on the authority of ‘Ali that the Prophet, sallallaahu ‘alayhi wa sallam, was at a funeral and commanded one of his companions to go to Madeenah and destroy every idol and level all graves. [Ahmad]
* Erecting crosses over the graves of Christians is an acknowledgment of their false beliefs. Even worse, this is a way of honoring their deviation and disbelief, and all this is prohibited. Al-Hijjaawi who is a senior scholar of the Hanbali School of Fiqh, mentioned that it is prohibited for a Muslim to follow the funeral of a non-Muslim or to burry him inside his grave because this is considered honoring him, and it is similar to performing a funeral prayer on him which is explicitly prohibited in the Quran.
In sum, it is prohibited for a Muslim to dig a grave for a non-Muslim as long as there are other non-Muslims to do this task. As for erecting a cross grave maker, this is prohibited in all cases.