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We have already issued Fatwa 89597 clarifying the ruling of appointing someone to slaughter on one's behalf.
As regards whether the appointer should slaughter the sacrifice after the 'Eed prayer in the country of the appointed person or in his own country (i.e. the country of the appointer), then the answer is that the sacrifice should be slaughtered after the 'Eed prayer in the country of the appointed person and not in the country of the appointer.
The Fiqh Encyclopaedia reads: “If the person who should slaughter the sacrifice resides in a country and he appoints another person who resides in another country to slaughter on his behalf, or that a person who is in another country appoints one to slaughter on his behalf in his own country, then what should be taken into account is the place where the sacrifice is slaughtered and not the place where the person who wants to slaughter is.”