If my 13 year old stepson wants to live with his father, my husband and his mom has shared custody, what does he need to do?

Children do not get to decide where they want to live unless the parents let them do that. There might need to be an agreement between the parties which would have to be approved by the court and an order of modification entered. But I do not know enough from your one sentence here to give the right directions. The best thing to do when there are legal problems is to have a full discussion with an attorney who handles those sorts of problems for a living.