Showing Filial Piety to One’s Parents After Their Death

Answer—and Allah is the One who grants success: That is valid and there is no objection to it. The scholars of the school, as in the marginal notes to Sharḥ al-Azhār, said: the worshipper must intend the gifting of the reward at the beginning of his prayer and his recitation.
Evidence for the soundness of this includes what is related from the Prophet (May Allah bless him and his family and grant them peace) concerning the revelation of His saying, Exalted is He: “And that there is not for man except that [good] for which he strives.” [Surah al-Najm:39]—that he said: “Indeed, a man’s child is part of his striving (earnings).”
And His saying, Exalted is He: “Indeed, We will record what they have put forth and their traces.” [Yā Sīn:12] If the child is righteous, the reward of his righteous deed reaches his parents—by virtue of their having caused his upbringing and education.
Yes, the reward of a righteous act can reach the deceased—whether from the child or from someone else—as indicated by what is narrated in the Majmūʿ of Imām Zayd b. ʿAlī, from his forefathers, from ʿAlī, peace be upon them all: that the Messenger of Allah (May Allah bless him and his family and grant them peace) heard a man pronouncing the talbiyah on behalf of Shubruma. He said to him, “Who is Shubruma?” He replied, “A brother of mine.” The Prophet (May Allah bless him and his family and grant them peace) said, “If you have already performed ḥajj (for yourself), then pronounce the talbiyah on behalf of Shubruma; but if you have not performed ḥajj, then pronounce the talbiyah for yourself.”
The Prophet (May Allah bless him and his family and grant them peace) did not inquire whether Shubruma had bequeathed that or not; rather, he commanded him to perform ḥajj for himself and then to perform ḥajj for Shubruma.
The scholars of legal theory say: “Omitting further inquiry where multiple possibilities exist has the force of generality in the wording.” Therefore, this ḥadīth indicates that righteous acts performed by others can reach the deceased—whether from a child or from someone else.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1