Is it permissible to exchange currencies over the phone by paying the amount later, and what is the necessity that makes usury permissible?

Exchanging currencies is considered a sarf (currency exchange) transaction and has specific rules. For exchanging a currency for the same type of currency, taqabudh (mutual possession) and tamathul (equality in quantity) are required. For exchanging it for a different type of currency, only taqabudh is required. What occurred between you two was a sarf transaction in which the condition of taqabudh was not met by both parties. The correct method is immediate taqabudh, such that the money is handed to the exchanger, and your agent receives it at the same time, or handing over the currency for which your agent will receive an equivalent amount from the exchanger's agent (the issue of suftajah - bill of exchange). There is no harm in transferring money in a way that lacks immediate taqabudh when there is a necessity. Necessity is defined as a situation that leads to perdition or significant harm.