What is the ruling on buying Saudi Riyals found in another country, with the equivalent in Egyptian Pounds being paid in the contracting session, given that the Riyals were not seized in the contracting session?

If your relative's brother is a party to the contract or an agent on their behalf, and your cousin is your agent, then the required قبض (seizure/possession) has occurred, and the contract was concluded via phone call. The Shariah standards for Islamic financial institutions stipulate that contracting through modern communication means, such as audio or video calls over the internet, takes the rulings of contracting between parties present, and all rulings applicable to in-person contracting apply to it, such as the 'contracting session' (مجلس العقد), which is the duration of the communication between the contracting parties as long as the discussion pertains to the contract.