Is it permissible for the buyer to authorize the seller's agent to sell the shares that he bought from him on credit, and to transfer the amount to his account, knowing that the seller's agent is the one who bought the shares in cash and deposited them in his private account?

If the second buyer is not the first seller—whether he directly purchased it himself or through his agent—then there is no harm. Otherwise, it is not permissible, as it is forbidden for the seller of goods on credit to buy them back from himself or through his agent, and such a transaction is invalid. It is also forbidden if the agent buys it for himself through a prior agreement and collusion with the first seller for it to return to him. However, if his father or son, or similar, buys it without stratagem, it is permissible and valid, because each of them is like a stranger with respect to the purchase.