Is it permissible in Sharia to exchange currencies in this manner, and is immediate possession or verification of the amount reaching the account required?

If you act as an agent for converting foreign currency amounts and delivering them to their recipients in local currency, this constitutes a money exchange (sarf), the validity of which requires possession of the two exchanged amounts in the contract session. If the amount reaches your account, then agree on the exchange rate and pay the equivalent in local currency. If a notification of the amount arrives but it has not yet been credited, it is permissible to pay its عوض (compensation/equivalent), but do not dispose of it until you are able to dispose of the amount in your account. The delay in bank crediting for commonly recognized periods is excused, provided that the beneficiary does not dispose of the currency during the excused period except after the effect of the bank crediting allows for actual receipt.