Very confused even after H1B approval! Please advice ..

[Aman]

Hi!,

 

I am currently working in an University on J-1. My present employer filed for H1B and my new H1B with the University Starts from July 1st. In the mean time, a private company also filed for a H1B on my behalf and got it approved. 

 

I want to start working for the private employer from December end. Here is my question:

I want to accept the H1B from my present employer (The University) and go for a Visa stamping in India in October. Then,  After I come back from India (with the University H1B visa stamped), I plan to resign from the University and start working for the private firm immediately. CAN I DO THAT? 

If I com back with a University H1B visa stamp, can I immediately start working for the private employer (without any more paper work / stamping) ?

 

Please kindly advice ...

 

Thanks a lot

 

Aman