Praise be to Allah.
If your cousin is working as an agent in return for a specific fee, then it is not permissible for him to pay from his own pocket on your behalf anything of the price of the goods, because that is combining a loan and a sale transaction, which is haraam according to the majority of scholars, because of the report narrated by at-Tirmidhi (1234), Abu Dawood (3504) and an-Nasaa’i (4611) from ‘Amr ibn Shu‘ayb, from his father, from his grandfather, who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “It is not permissible to arrange a loan combined with a sale transaction.” This hadith was classed as saheeh by at-Tirmidhi and al-Albaani.
The word translated as “a sale transaction” includes all kinds of business transactions including brokerage or acting as an agent in return for a fee.
Therefore you must give him the price of the goods beforehand, in full or more than that.
If he acts as an agent for nothing in return, then there is no problem with him paying on your behalf.
If your cousin is a partner, it is permissible for him to pay the price of the goods, or part of it, according to whatever you have agreed upon.
Whether he is an agent or a partner, in either case he is your proxy in exchanging currency and paying the price of the product and customs fees. The partner acts on his own behalf and on behalf of his partner as a proxy.
Based on that, if you gave him the money in Egyptian pounds, and he went and changed it to dollars, then he is acting as a proxy and a trustee, whether he exchanged it for a large or small amount of dollars. In this case, you should make note of the amount you paid in Egyptian pounds, then settle the account on that basis later on.
So if you gave him one hundred thousand pounds, and he went and exchanged it and paid in dollars, then when you want to settle the account, you should look at what you gave him, which is one hundred thousand pounds, and there is no need to mention the issue of exchange.
If you give him the money in dollars, then you should make note of what you gave him in dollars, and settle the account on that basis.
So if you give him ten thousand dollars, and what is required of him when settling the account is to pay that amount, then when settling the account you may say to him: What is required from you is ten thousand dollars, or half of that, for example, then he may pay it either in dollars or in Egyptian pounds, on the basis of the exchange rate on the day when the account is settled. Thus he should pay you in pounds the amount that will enable you to buy the required amount of dollars on that day.
The same applies if he contributed to the business by paying from his own pocket in dollars. When you settle the account with him, he may ask you to pay him the same amount in dollars, so you may either pay the same amount of dollars or pay him in Egyptian pounds in accordance with the exchange rate on the day of settling the account.
What matters in this situation is the exchange rate on the day you settle the account, not on the day when the payment was made.
If there are some details in your business dealings which require an answer that is not given here, or if the situation is different from the scenarios that we have discussed, please explain it to us so that we may give you an appropriate answer.
And Allah knows best.