Praise be to Allah.
It is permissible for the Muslim to appoint another Muslim to slaughter the udhiyah on his behalf.
It says in al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (5/105-106):
The fuqaha’ are agreed that it is valid to appoint someone else to slaughter the udhiyah on one’s behalf, if the person appointed is a Muslim.
But it is best for him to slaughter it himself, except in cases of necessity.
The majority are of the view that the udhiyah is valid, even though it is makrooh (disliked), if the one who is appointed to slaughter it is a kitaabi (one of the People of the Book, i.e., a Jew or Christian), because they are people whose meat it is permissible to eat. End quote.
For more information, see the answer to question no. 175475.
It is proven that there is a specific time for slaughtering the udhiyah, and it cannot be offered at any other time. That time begins after the Eid prayer, so whoever slaughters his udhiyah before that, it is not valid as an udhiyah.
It was narrated that al-Baraa’ (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) said: The first thing with which we begin on this day of ours is the prayer; we pray then we go back and offer the udhiyah. Whoever does that has acted in accordance with our Sunnah, and whoever has already slaughtered (the sacrificial animal), that is just meat that he has given to his family, and there is nothing of the udhiyah in it.” Narrated by al-Bukhaari (5545) and Muslim (1961).
Ibn ‘Abd al-Barr (may Allah have mercy on him) said:
The scholars are unanimously agreed that the udhiyah is to be done at a specific time…
They are unanimously agreed that the slaughtering of the udhiyah, for those who are not travelling, is not valid if done before the prayer, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever slaughters (the sacrificial animal) before the prayer, that is just a sheep for meat.” End quote from al-Istidhkaar (15/148).
If there is a difference in time between the countries of the one who was appointed to slaughter the udhiyah and the one who appointed him, then what counts is the country where the one who was appointed is.
The Permanent Committee for Scholarly Research was asked:
Someone has come to us with a question in which he says: a relative of his is staying in the USA for medical treatment, and he has appointed him to buy and slaughter his udhiyah here in Saudi Arabia. He is asking: is it permissible for him to slaughter this udhiyah with his own udhiyah after offering the Eid prayer, and before the time for the Eid prayer begins for his relative in the United States, based on the hadith in which the Prophet (blessings and peace of Allah be upon him) said, “The fast is the day when you [Muslims] fast, the breaking of the fast is the day when you break the fast, and the sacrifice the day when you offer the sacrifice”? If he did that, what must he do now?
They replied: It is permissible for the one who was appointed to offer the udhiyah to slaughter the udhiyah of the one who appointed him after the (time of) Eid prayer for the one who was appointed to do that, not of the one who appointed him, because the one who was appointed is acting in the stead of the one who appointed him.
It does not matter if the udhiyah is slaughtered before the time of udhiyah begins in the country where the one who appointed him is staying.
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions.
Permanent Committee for Scholarly Research and Ifta.
Saalih ibn Fawzaan al-Fawzaan, ‘Abdullah ibn ‘Abd ar-Rahmaan ibn Ghadyaan, ‘Abd al-‘Azeez ibn ‘Abdillah ibn Muhammad Aal ash-Shaykh, ‘Abdullah ibn Muhammad al-Mutlaq, ‘Abdullah ibn ‘Ali ar-Rukbaan, Ahmad ibn ‘Ali Siyar al-Mubaaraki. End quote.
If he delays it until the time of Eid prayer begins in the country where the one who appointed him is staying, that is fine, because the time for offering the udhiyah lasts until the end of the days of at-tashreeq (11th, 12th and 13th of Dhu’l-Hijjah).
And Allah knows best.