You need to have your H1 for stamping, to prove you are on status, driver's license etc.
If the H1 approval has your name on it you have the right to keep it.
If the employer does not give you H1, tell them you are going to stop working - you will be surprised the impact that will have on their descion to keep your H1 approval to themselves. If the H1 approval does not have I-94 on it, you may be out of status.