What should I do after my father's death?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Abu Usayd Maalik ibn Rabeeʻah As-Saaʻidi said:

“While we were with the Prophet a man from the Banu Salimah came to him and said, ‘O Messenger of Allah, is there any way of honoring my parents that I can still do for them after they die?’ He said: ‘Yes, to pray for them, to supplicate for their forgiveness, to fulfill their promises after their death, to maintain the ties of kinship which cannot be maintained except through them, and honour their friends.’” [Abu Daawood]

Your duty towards your father after his death is to supplicate Allah for him and ask Allah to forgive him and bestow His Mercy on him.

Allah Says (what means): {… and say, “My Lord, have mercy upon them as they brought me up [when I was] small.”} [Quran 17:24]

Abu Hurayrah narrated that the Prophet said: “When a person dies, his deeds come to an end, except for three: a continuous charity, knowledge that benefits people and a pious child who supplicates for him.” [Muslim]

The Prophet also said: “The noblest deed is that a person should be benevolent towards his father's friends after his death.” [Muslim]

As for other good deeds like the recitation of the Quran and presenting its reward to a dead person and other good deeds, then Muslim scholars differed in opinion concerning this issue.

However, we conclude that everyone who performs a good deed he deserves the reward of that act. Whenever one owns the reward of something he can present it to others. If the person whom the reward is presented is Muslim he will receive it.

Anyway, beware of innovations invented by many people and being practiced by many Muslims such as ceremonial gatherings after the death of the person to mourn him, preparing food for people, setting a stage for the reception of visitors, etc.; all the above matters are not permitted in the Sharee’ah.

To know how to be kind and dutiful to the parents after their death, please refer to Fataawa 82254, 91983, 395335, 303685, 83233 and 120936. You may aslo refer to the following article: Ingratitude towards parents
Allah knows best.