I am a postdoc from one university. My non cap H1B is going to valid until 08/27/2020 and I94 is valid until 09/04/2020, but my current contract is going to end at 02/16/2019.
When I first started my postdoc job here at 08/2017, the first contract was going to end at 06/31/2018, but they applied the H1B with three years until 08/27/2020 for me.
Since the first contract, the contract has been extended three times until 02/16/2019. I have found another university who would like to sponsor my H1B and they should complete the H1B transfer before 02/16/2019.
The current job asked me to sign a resignation letter to confirm that my current job is going to end after 02/16/2019. Should I do it if I want to use the 2 month grace period just in case that the new university cannot make it before the deadline?
If no, what is your advice here? If yes, what should I do? Should I contact the international office from the new university to ask them to send the petition letter on my behalf if they cannot make the deadline?
Thanks very much in advance.