What is the ruling on money transfers from Britain to Iraq, where the British Pound is converted to US Dollars, then received in US Dollars in Iraq after several days?

There is no objection to the remitter buying dollars from the money changer and then authorizing the money changer to deliver them to Iraq, and paying him a fee for that. This is because the exchange of currencies, which is a condition for the permissibility of currency exchange, has implicitly occurred between the remitter and the money changer.