Allah Almighty says: {And [there is a share for] those who came after them, saying, “Our Lord, forgive us and our brothers who preceded us in faith.} [Surat al-Hashr: 10]
Supplicating for the believers as a whole is one of the rights of Muslims upon one another, and the best people to supplicate for are the Prophet’s Companions. So, if you see a person saying after mentioning the name of a Companion, “may Allah be pleased with him/her” and loving the Companions and asking Allah’s forgiveness for them, then you should know that he is a follower of the Sunnah and sound guidance. On the other hand, if a person hates them or speaks ill of them, this is a sign that he is a religious innovator who has gone astray and who has no share of the Sunnah. The Companions (may Allah be pleased with them) were the channel through which the religion was conveyed to the Ummah. So, a person who discredits them is actually discrediting the Shariah.
948/1 - ‘Ā’ishah (may Allah be pleased with her) reported that a man said to the Prophet (may Allah’s peace and blessings be upon him): “My mother has died suddenly. I think that if she were able to talk, she would have given charity. So, if I give charity now on her behalf, will she get the reward?” The Prophet replied: “Yes.” [Narrated by Al-Bukhāri and Muslim]
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1) It is legitimate to give charity on behalf of a dead person, and it is recommended to do this quickly so that the reward can reach him fast.
2) Giving charity on behalf of either parents is part of dutifulness to him or her after their death.
3) It is glad tidings to the believers that their deeds do not cease with their death, and that their righteous children remaining after them is an ongoing source of reward for them.
4) The Companions (may Allah be pleased with them) were keen to adhere to the texts of the Qur’an and the Prophet’s guidance. That is why the Companion in the Hadīth did not hasten to give the charity, though it was apparently something good, before he asked the Prophet (may Allah’s peace and blessings be upon him) about it.
949/2 - Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah’s peace and blessings be upon him) said: “When a person dies, his deeds come to an end except for three things: ongoing charity, beneficial knowledge, or a pious child who supplicates for him.” [Narrated by Muslim]
1) Out of the mercy of Allah towards His believing servants, He has enabled them to benefit from the reward of the deeds they began during their life even after death.
2) We should be keen to raise righteous children, for their righteousness is good for them and us, as they will supplicate for us after we die.
3) Useful knowledge is the best thing a person can leave behind, for it endures for as long as Allah wills. Ongoing charity may come to an end one day, and a person’s righteous children will eventually die. So, beneficial knowledge is unparalleled in this regard, if the intention behind it is sincere. It is "the immortal child", as some scholars called it.
Al-Nawawi (may Allah have mercy upon him) said: “The scholars said: The Hadīth means that a person’s deeds come to an end with his death, and so do the rewards for his deeds, except in the three things specified in the Hadīth, given that he was the reason behind them. His children come and grow up due to his earning, and so does the useful knowledge he leaves behind in the form of teaching or books. Likewise, the ongoing charity is the endowment he has made. This points out the significance of getting married in the hope of having righteous children and also indicates the merit and great rewards of endowments and knowledge. We are thus encouraged to seek more and more knowledge and leave it behind through teaching, writing, or explaining. This also tells us that we should seek the most useful branches of knowledge and then the next most useful.” [Commentary on Sahīh Muslim]
Al-Subki (may Allah have mercy upon him) said: “And writing books, of knowledge, is more effective, given that it endures throughout the passage of time.” [Fayd al-Qadīr Sharh al-Jāmi‘ al-Saghīr]