Is it permissible to appoint someone to slaughter and distribute the Hadi (sacrificial animal) outside the Kingdom on behalf of the deceased father, in order to identify those most in need?

The madhhab of the majority of scholars is that it is obligatory to slaughter the compulsory sacrificial animal (hady) and distribute it within the Sacred Precinct (Haram). Their evidence is the hadith: "All the mountain passes of Mecca are a path and a slaughtering place," and His (Allah's) saying: "Then its destination is the Ancient House" (22:33). This is also because the Prophet, peace and blessings be upon him, slaughtered his sacrificial animal in Mina. The author of Al-Furu' indicated that the obligation of slaughtering within the Haram is by agreement of the four Imams.

Whoever slaughters outside the Haram, their sacrifice is not valid, and they are required to repeat it within the Haram.

Al-Shirazi stated in Al-Muhadhdhab: If a pilgrim in a state of ihram is obligated to offer a sacrifice (dam) due to ihram, it is obligatory for them to give it to the poor of the Haram, based on His (Allah's) saying: "an offering, reaching the Kaaba" (5:95). If they slaughter it outside the Haram and bring it into the Haram: 1. If it has changed and become putrid, it is not valid. 2. If it has not changed, there are two views: it is not valid, and it is valid. The more cautious approach is to disallow it.

Therefore, it is obligatory for you to slaughter your compulsory sacrificial animal in Mecca, or to appoint someone to slaughter it there on your behalf.