All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The matter is as you mentioned in the question that if there is a difference between the currencies when exchanging money, then it is a condition that it should be hand to hand, but it is not a condition to be the same amount as the Prophet said: “…Take what was from hand to hand and leave what was on credit….” [Al-Bukhari] Moreover, the narration reported by Muslim reads: “…If these classes differ, then sell as you wish if payment is made hand to hand.” In addition to this, we have mentioned the conditions that should be met when exchanging money in Fatwa 83372.
As regards transferring a currency from one country to another, then there is no doubt that it lacks the condition of ‘hand to hand’ exchange. The Fatwa [the view] we adopt here in Islamweb is that this prohibition may be avoided if the money changer gives a certified cheque or a bill of exchange in the other currency to the person who wants to transfer money. This method is considered as ‘hand to hand’ according to a group of contemporary scholars. For instance, the Islamic Fiqh Academy of the Muslim World League is of the view that receiving the cheque is like receiving money directly (from hand to hand) when the conditions of exchanging currencies are met in exchange offices. Similarly, some scholars are of the view that immediate exchanging may be conducted through the phone, in a way that you give the money changer an amount at a time when you agree with one of your family members to be present at the agent of this money changer and when you give the money to the money changer, his agent will give the exchange of that amount in the other currency to your family member at the same time. It may be that the urgent need for such a transaction makes this procedure permissible.
However, there is a great doubt in such a transaction and many scholars are of the view that it is not permissible. Therefore, this transaction should not be taken as a profession by which one earns his living because this is not often a necessity for whoever takes it as a profession.
Allaah Knows best.