Re-stamping H-1 to F-1 to H-1

You should consider whether it will help you to get the passport stamped and extended, but it is not necessary.

An unexpired H1-b stamp may be used if you currently are in H1-b status with a new employer. You need to prove it, upon request. Bring a copy of your Approved change of status to the new employer. Make a photocopy of the last I-94 from your newest I-797 form before you hand it in at the airport. Keep the approval notice and present it upon request. You can also get a letter from your newest employer indicating that you are still employer with it.

If you request an H1-b stamp outside of the U.S., then you have to obtain and present a certified copy of your application record from the office that prepared it. The changes of status may need to be shown, but may be documented in the last filing.

You should schedule an appointment with an experienced immigration and visa ttorney to discuss the situation.