Ring the company up and ask for this information in writing if you havent already.
Your daughters ex would be mad to allow the finance to continue in his name because your daughter could stop paying and ruin his credit rating. I would also be concerned about the ownership of the vehicle, the ex could claim at some point in the future that the car is still his? I doubt he would be able to change the owners details without consulting the finance company because he is in theory selling the car and the debt.
I would get this all in writing, your daughter may have just spoken to someone who isnt totally up on the legalitys of what they are suggesting!