The most important thing that will benefit someone after his death is du`aa for him, to ask for forgiveness and mercy for him and for salvation from the Fire and entrance into Paradise.  The Prophet (ﷺ) gave us examples of such supplications.

1. "O Allah, forgive our living and our dead, our present and our absent, our young and our old, our males and our females. O Allah, whoever You keep alive of us – keep him alive on Islam; and whoever You take in death of us –take him in the faith. O Allah, deprive us not of the reward for him and let us not go astray after him."1

2. "O Allah, forgive him and have mercy upon him, free him from all evil and pardon him, make his accommodation honorable and expand his entrance. Wash him with water, snow and hail, and purify him as You have purified the white garment from dirt. Give him in place of his home a better home and for his family a better family and for his spouse a better spouse. Admit him to Paradise and protect him from the punishment of the grave and the punishment of the Fire."2

3. "O Allah, so-and-so [mentioning his name] is under Your protection and in Your proximity, so protect him from the trial of the grave and the punishment of the Fire. You are the one of fidelity and truth, so forgive him and have mercy upon him. Indeed, it is You who is the Forgiving, the Merciful."3

4. "O Allah, Your servant and the son of Your female servant is in need of Your mercy, and You have no need to punish him. If he was good, then increase his reward; and if he was bad, then overlook what he did."4

1 Aḥmad and Ibn Mājah – ṣaḥeeḥ.

2 Muslim.

3 Ibn Mājah and Abu Dāwūd - ṣaḥeeḥ.

4 Al-Ḥākim and aṭ-Ṭabarāni