The First Topic: The Ruling of Agency in Exchange
Agency in exchange is permissible.
The Evidences:
Firstly: From consensus. Ibn al-Mundhir [473] -It was reported from him by Ibn Ḥajar; Ibn Ḥajar said: 'Ibn al-Mundhir stated: "They all agreed that agency in currency exchange is permissible, even if a man appoints one to exchange dirhams for him and appoints another to exchange dinars for him, and they meet and conduct a valid exchange according to its conditions; that is permissible.'" See: "Fatḥ al-Bārī" (4/481). and Ibn al-Qattan [474] -Ibn al-Qaṭṭān said: "All those whose opinions are preserved among the scholars have agreed that agency in currency exchange is permissible.'" See: "Al-Iqnāʿ" (2/157) reported this consensus.
Secondly: Because agency is permissible in all types of sales, and exchange is a type of sale [475] -See: "Iqna'a" by Ibn al-Mundhir (2/705). .

Thirdly: Because receiving in exchange is part of the validity of the contract, and it is valid from someone present at the time of the contract, which is the agent [476] -See: "al-Bināya" by al-ʿAynī (9/241). .
Fourthly: Because the agent’s receiving is equivalent to the principal’s receiving [477] -See: "Kashshāf al-Qināʿ" by  al-Buhūtī (3/266) .
The Second Topic: The Agent Receiving Before the Principal Departs
If the two transacting parties appoint an agent for receiving, and the receiving occurs before they separate, the contract is valid, according to the agreement of the four Islamic Jurisprudential schools: Hanafi [478] -  "Hāshiyat Ibn ʿĀbidīn" (5/515); "al-Fatāwā al-Hindiyya" (3/242) , the accepted view among the Malikis [479] -See: "al-Tāj wal-Ikleel" by al-Mawwāq (4/310); "Mawāhib al-Jaleel" by  al-Hattāb (6/135- 136) , Shafi'i [480] -"al-Majmūʿ" by al-Nawawī (9/404). , and Hanbali [481] -"Kashshāf al-Qināʿ " by al-Buhūtī (3/266);  "Sharḥ Muntahā al-Irādāt" by al-Buhūtī (2/73). ; because receiving pertains to the contractor, either he receives himself or through his agent in his presence [482] -"Sharḥ Muntahā al-Irādāt" by al-Buhūtī (2/73). .
The Third Topic: The Agent Receiving After the Principal Departs
If the two parties appoint someone to receive on their behalf, or one of them appoints someone to receive for him, and then the two agents or the principal and the second contractor separate before receiving, the exchange becomes void, according to the agreement of the four Islamic Jurisprudential schools: Hanafi [483] -"Hāshiyat Ibn ʿĀbidīn" (5/515); "al-Fatāwā al-Hindiyya" (3/242) , the accepted view among the Malikis [484] -See:"al-Tāj wal-Ikleel" by al-Mawwāq (4/310);  "Mawāhib al-Jaleel"by al-Hattāb (6/135- 136). , Shafi'i [485] -See: "al-Majmūʿ" by al-Nawawī (9/404). , and Hanbali [486] - "Kashshāf al-Qināʿ" by  al-Buhūtī (3/266); "Sharḥ Muntahā al-Irādāt" by al-Buhūtī (2/73) ; because receiving pertains to the contractor; either he receives himself or through his agent in his presence [487] -See: "Sharḥ Muntahā al-Irādāt" by al-Buhūtī (2/73). .