If a son performs a righteous deed, will he be rewarded for it, and will his deceased father receive a reward similar to his because he is his son? And if a son is blessed with righteous offspring, will he be rewarded for their good deeds, and will his father also be rewarded?

A person's deeds cease upon their death, except for three: ongoing charity (sadaqah jariyah), knowledge from which others benefit, or a righteous child who prays for them. Likewise, some good deeds continue to benefit a believer after their death, such as: knowledge they taught and spread, a righteous child they left behind, a copy of the Qur'an they bequeathed, a mosque they built, a house they built for a wayfarer, a river they caused to flow, and charity they gave from their wealth during their health and lifetime.

If a father guides his son to a good deed, he is rewarded for it, because "the one who points to good is like the one who does it," and this falls under spreading beneficial knowledge. So, the father is rewarded for what he was the cause of in his son's action, not for every good deed his son performs.

Therefore, the son should frequently supplicate for his father and give charity on his behalf if he is able, or make an endowment for him to be an ongoing charity for him.