The Adhha sacrifice is legislated on behalf of the Living Person or the Deceased

Question :

Is it permissible to perform the Adhha sacrifice for the deceased? I would like some clarification of the evidence. Also, what is the ruling on giving its value in money in charity?

Answer:

The Adhha sacrifice is legislated on behalf of the living and the deceased. This is because the Prophet used to perform the Adhha sacrifice with one sheep for himself and his family members in Al-Madinah, and some of them were deceased like Khadijah and his two daughters, Ruqayyah and Umm Kulthum. This is also because it is an act of charity and drawing near (to Allâh), so it is similar to all the other types of charity. It is stressed more for the living due to the Prophet's action and his statement:
"When the month of Thul-Hijjah enters and one of you wants to perform the Adhha sacrifice, he should not remove any of his hair or nails."

This was recorded by Muslim in his Sahih from a Hadith of Umm Salamah.

In reference to what some of the Fiqh scholars have mentioned regarding this issue of the prohibition of the person for whom the sacrifice is being performed removing any of their hair or nails, I do not know of any evidence for it that is reliable. Only the person who is performing this Adhha sacrifice for himself, who sacrifices the animal from his wealth is addressed with this command. In reference to his wife and his children, they are not prohibited from removing any of their hair or nails, because they are not offering the sacrifice. The sacrifice is only being performed on their behalf by the one who takes care of them, so he is the one addressed with this prohibition.

Slaughtering the animal is better than giving charity with its price due to what that contains of reviving the Sunnah and manifesting it, and following the Prophet and his Companions. And Allâh is the Giver of success.

Source:
Ash-Shaykh Ibn Baz
Fatawa Islamiyah, Vol. 4 Pages 331-332