Praise be to Allah.
Your selling the dollars in your account to your brother in return for local currency is called an exchange, and the condition of it being permissible is that the exchange should take place immediately.
The exchange can be either real, meaning that the money is exchanged hand-to-hand, or it may be virtual, meaning that the money goes into the account of each of you.
The basis for stipulating that the exchange take place immediately is the report narrated by Muslim (1587) from ‘Ubadah ibn as-Samit (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “: “Gold for gold, silver for silver, wheat for wheat, barley for barley, dates for dates, salt for salt, like for like, same for same, hand to hand. But if these commodities differ, then sell as you like, as long as it is hand to hand [that is, exchanged immediately].”
Paper currencies come under the same rulings as gold and silver.
It said in a statement of the Islamic Fiqh Council belonging to the Organisation of the Islamic Conference (OIC):
With regard to the rulings on paper currencies, they are legal tender by which prices are measured, and they come under the established Islamic rulings on gold and silver with regard to matters such as riba (usury), zakah, payment in advance (salam transaction) and so on.
End quote from Majallat al-Majma‘ (issue no. 3, vol. 3, p. 1650; issue no. 5, vol. 3, p. 1609).
Based on that, it is not permissible for you to take local currency from your brother when there is a delay in the dollars being deposited in his account.
But it is permissible for you to send the dollars to him to keep as a trust for you, then once the dollars have been deposited in his account, it is permissible to do this exchange, whereby he will take possession of the dollars and you will take local currency from him at the rate of exchange on that day.
It says in Kashshaf al-Qina‘ (3/269): If he gives him five dirhams for half a dinar, then he gives him a dinar for him to take half of it, the exchange is valid because it takes place immediately, even if he does not give him back half a dinar before they part.
So the half dinar is his, and the other half is like a trust in the hand of the recipient, because of what was noted above.
And they may separate before he gives him back the other half of the dinar.
Then if he wants to exchange the other half for what is left of the dinar with him, that is permissible.
Or if he buys something from him with the remaining half dinar, that is permissible.
Or if he wants to make the remaining half-dinar payment in advance for something, that is permissible, because it is his money and is not a loan that he gave to the other man.
Or if he wants to give it as a gift to the other man, so he lets him keep the remaining half dinar, that is permissible, because he is the owner of the wealth and is disposing of it in an appropriate manner. End quote.
This indicates that it is permissible to leave wealth with someone else as a trust, then exchange it for a different currency.
And Allah knows best.
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