Is it permissible to take a sum that was canceled from the university's invoice without the knowledge of the sponsoring entity, knowing that it will be recorded as a debt on the student?

The agent is entrusted, so it is not permissible for you to take the amount you saved. Rather, it must be returned to your university unless they grant you permission to take it. As for the costs of transferring money, for which you are not responsible, you may count them from the amount.