Is it permissible for the buyer to sell what he has bought before taking possession of it if the seller authorizes that, and then the seller completes the buying and selling process after a month?

If your cousin took possession of the car and then appointed you as his agent to sell it to another person, the sale is valid and permissible. This falls under the category of Tawarruq (monetization). Your cousin's authorization of the buyer to sell it for a deferred payment does not affect its validity. However, if you sold the car before your cousin took possession of it, then it is not permissible, due to the saying of the Prophet (peace be upon him): "If you buy something, do not sell it until you take possession of it."