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 is His slave and Messenger.
The issue of a dead hearing the speech of the living is an issue over which the scholars differed in opinion. Indeed, we have already issued Fataawa 23015, 85320 and 87936 clarifying this difference of opinion and mentioning the preponderant view.
As regards what is confirmed about what to do for a person who breathes his last, then it is to advise him to say La Ilaaha Illa Allaah (None has the right to be worshipped but Allaah) as clarified in Fatwa 82779. It seems that this is what you meant by saying that it has been confirmed in some Ahaadeeth in Saheeh Muslim and other books of Hadeeth.
As regards teaching the dead "La Ilaaha Illa Allaah" in his grave, a Dha’eef (weak) Hadeeth was reported about this; Al-‘Ajalooni said in his book “Kashf Al-Khafaa’”: "The author of Al-La’aai Al-Masnoo’ah (i.e. As-Suyooti ) said: “As regards teaching the dead La Ilaaha Illa Allaah after burial, there is a Hadeeth reported by At-Tabaraani about it in his Mu’jam, but its chain of narration is weak.”
Allaah Knows best.