What is the ruling on working as a financial intermediary or an exchange agent between electronic banks, given the doubts about the source of clients' funds?

It is not obligatory to inquire about the source of clients' dubious funds in order to deal with them in a permissible transaction, for the Prophet, peace and blessings be upon him, dealt with the Jews. The basic principle is that what is in a Muslim's possession is his property until proven otherwise. If the customer wants to convert an amount from his electronic account to cash, and you withdraw the amount from your account and give it to him in cash for a commission, this is permissible.