Is it permissible for a brother to sell an item on credit to someone, then for the questioner to buy this item from the buyer with his money and include his brother as a partner in the sale without the brother having to pay anything for it?

I understand that you bought an item that your brother sold on credit, then you made your brother a partner in it, either through sale or a gift. There is nothing wrong with this, because your brother is allowed to buy back an item he sold on credit from someone other than the original buyer. So, he is allowed to buy it from you or accept it as a gift. A condition for this to be permissible is the absence of any suspicion of collusion, such as if the second sale occurred in the same sitting as the first sale; in that case, it would be prohibited.