Selling a purchased item before taking possession of it and taking it to one’s location
Question

I asked my cousin to buy me a car, because he deals in cars, and he found a good car for me. Then a customer came to him to buy it, and he sold it to him at a profit of $150. He kept fifty dollars and gave me one hundred dollars, and said: This is for you. I said: I have no right to it, because I did not pay the price of the car and I did not buy it. Do I have to accept this profit just because he said to me: This is for you? Did the car become my property?
Praise be to Allah.If you did not buy the car, it was still your cousin’s property, and the profit that was made is his. If you bought the car and he sold it without your permission, then this is improper conduct but the sale is valid if you allow it, and the entire profit is yours.
His saying that it is yours is not sufficient for the transaction to be concluded, unless the conditions for validity of the transaction were met. These conditions are:

The offer and acceptance, in any terms that are customarily used between people when buying and selling.
The price should be known; the transaction is not valid when the price is unknown.
The item being sold should be known, by seeing it or by means of a description which makes it known.

If these conditions were not met, then the transaction was not valid.
Moreover, the one who buys an item is not allowed to sell it until he takes it away from the original seller’s place, because the Prophet (blessings and peace of Allah be upon him) said to Hakim ibn Hizam: “If you buy an item, do not sell it until you take possession of it.” Narrated by Ahmad, 15316, and an-Nasa’i, 4613; classed as sahih by al-Albani in Sahih al-Jami`, 342.
Ad-Daraqutni and Abu Dawud, 3499, narrated from Zayd ibn Thabit that the Prophet (blessings and peace of Allah be upon him) forbade selling goods where they were bought, before the merchants moved them to their places. This hadith was classed as sahih by al-Albani in Sahih Abi Dawud.
The correct view is that this includes all types of trade goods. This is the view of ash-Shafa`i.
An-Nawawi (may Allah have mercy on him) said regarding the scholars’ view on selling an item before taking possession of it:
We have stated that our view is that it is invalid in all cases, whether the item is food or anything else. This is the view of Ibn `Abbas; it was soundly narrated from him and Muhammad ibn al-Hasan.
And he said: In the case of goods that are portable, such as lumber, grains, fish and the like, taking possession of it means moving it to a place that does not belong to the seller, whether it is moved to the property of the purchaser, or to desolate land, or a street, or a mosque, or anywhere else.
End quote from al-Majmu`, 9/270, 276.
For more information, please see the answer to question no. 39761.
If your cousin gave you some of the money to appease you, because he sold what he had promised to sell to you, there is nothing wrong with you accepting it.
And Allah knows best.