What can benefit the deceased after his death?

The principle is that the dead do not hear the words of the living, because Allaah says (interpretation of the meaning): "… but you cannot hear those who are in graves." [Faatir 35:22] and

"Verily, you cannot make the dead to hear…" [al-Naml 27:80]

The Prophet (peace and blessings of Allaah be upon him) said: "When a person dies, all his deeds come to an end except three: sadaqah jaariyah (ongoing charity, e.g. a waqf or endowment), beneficial knowledge (which he has left behind), or a righteous child who will pray for him." (Reported by al-Tirmidhi, no 1376; he said this is a saheeh hasan hadeeth)

Prayers for forgiveness offered by both sons and daughters of the deceased bring great benefits, as the Prophet (peace and blessings of Allaah be upon him) said: "A man’s status will be raised in Paradise and he will ask, ‘How did I get here?’ He will be told, ‘By your son’s du’aa’s (prayers) for forgiveness for you." (Reported by Ibn Maajah, no 3660; see also Saheeh al-Jaami’, 1617)

‘Aa’ishah (may Allaah be pleased with her) reported that a man said to the Prophet (peace and blessings of Allaah be upon him): "My mother has passed away, and if she could have spoken, she would have given something in charity. Will she receive a reward if I give something on her behalf?" He said, "Yes." (Reported by al-Bukhaari, Fath, 1388)

Abdullaah ibn Buraydah reported that his father (may Allaah be pleased with him) said: "While I was sitting with the Messenger of Allaah (peace and blessings of Allaah be upon him), a woman came to him and said: ‘I gave my mother a slave-woman in charity, and now my mother has died.’ He said: ‘You have got your reward, and your right of inheritance has brought your gift back to you.’ She said, ‘O Messenger of Allaah, she still had one month to fast – can I fast it on her behalf?’ He said, ‘Fast it on her behalf.’ She said, ‘She never went to Hajj – can I perform Hajj on her behalf?’ He said, ‘Perform Hajj on her behalf.’" (Reported by Muslim, may Allaah have mercy on him, in his Saheeh, no. 1149)

This shows that it is also permissible to fast on behalf of the deceased

Other deeds that may also benefit the deceased are Hajj and ‘Umrah on their behalf, after the living person has first performed Hajj and ‘Umrah on his or her own behalf.

Another thing that may benefit the deceased is to fulfil their nadhr (vow), because Ibn ‘Abbaas (may Allaah be pleased with him and his father) reported that a woman came to the Prophet (peace and blessings of Allaah be upon him) and said: "My mother made a vow to perform Hajj but she died before she could do it. Can I perform Hajj on her behalf?" He said, "Yes, perform Hajj on her behalf. Don’t you think that if your mother owed a debt you would pay it off?" She said, "Yes." He said, "Then pay off what is owed to Allaah, for Allaah is more deserving of having vows fulfilled." (al-Bukhaari, al-Fath, 7315)

Things that benefit the deceased after his /her death

1.A righteous child who will pray for him
2.sadaqah (charity) given on his behalf

3. Hajj and ‘Umrah on their behalf

4. fast on behalf of the deceased

I ask Allaah to forgive have mercy  on all the deceased Muslims, for He is the Forgiving, Most Merciful