Is it permissible by Sharia to pay a sum of money to help a relative involved in an embezzlement case return to his job and avoid prison?

If your cousin repents sincerely from embezzlement, there is no impediment to helping him find a suitable job, as long as it is believed that he will not return to embezzlement, and so that his unemployment does not become a tool for Satan against him. However, striving to reinstate him in a usurious bank is not permissible, due to the assistance it provides in sin, and means are judged by their ends. Just as it is not permissible for him to work there, it is not permissible for you to intercede or pay money to reinstate him there, in accordance with the Almighty's saying: "Whoever intercedes with a good intercession will have a share of it, and whoever intercedes with a bad intercession will have a share of it. And Allah is over all things a Maintainer." But if you exert effort or spend money to find him a permissible job, that would be an act for which you would be rewarded, based on the hadith: "Allah is in the aid of His servant as long as the servant is in the aid of his brother."