Is it permissible to offer an Udhiyah on behalf of the deceased, and which of the two is better: offering the Udhiyah on their behalf or donating its value in charity?

The Udhiyah (sacrifice) is a Sunnah for the living. However, if a deceased person bequeathed it from one-third of their wealth or endowed it, then their will and endowment must be executed. If they did not bequeath or endow it, and one of their relatives or others wishes to offer a sacrifice on their behalf, it is good and considered charity for them. It is not a condition to offer a separate sacrifice for each deceased person; rather, it is permissible to include many deceased persons, or both living and deceased family members, in its reward. It is also permissible to donate the monetary value of the Udhiyah on behalf of the deceased, and this might even be more preferable, unless it is known that the deceased was deeply attached to the Udhiyah and wished that someone would sacrifice on their behalf after their death. In that case, the Udhiyah would be more preferable, due to the piety it entails towards them and the fulfillment of their wish.