Burying a deceased, offering Du`a' for him, and asking Allah to forgive and keep him steadfast
Acts authentically reported from the Prophet (peace be upon him) after burial include offering Du`a', asking for Allah Forgiveness, and begging steadfastness for the deceased.
`Uthman ibn `Affan (may Allah be pleased with him) reported:
Whenever Allah's Messenger (peace be upon him) finished burying the deceased, he would stay with them (i.e. by their graves) and say: "Seek forgiveness for your brother and beg steadfastness for him, for he will be questioned now."
Abu Dawud in his Sunan (Hadith compilation classified by jurisprudential themes) and by
Al-Hakim, who ranked it as Sahih [authentic]) As for the question about
reminding the deceased to say “La ilaha illa Allah (there is no god but Allah)” after burial, it has no basis in either the Qur'an or the Sunnah (whatever is reported from the Prophet). It is a Bid`ah (innovation in Islam).
Ibn Al-Qayyim (may Allah be merciful to him) said: "The Prophet (peace be upon him) would neither recite the Qur'an nor remind the deceased to say: “La ilaha illa Allah", while standing by their graves. Moreover, the Hadith regarding this act is not authentically reported."May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.