employer asking to submit approved petition on resignation. should i hand it over?

[prashastsaxena]

I am serving notice period of employer A through which I went to USA on H1B from Mar 2014 - Oct 2016 and returned back to India in Oct 2016. My petition was first approved in Sep 2013.
On resignation, my employer asked me to surrender original approved H1B petition.
Should I be submitting it to them?

would I be able to apply for cap-exempt H1B before Sep 2019 (6 years following initial approval i.e. Sep 2013) through employer B? If yes, would they require my original H1B petition to submit cap exempt application? and do they have to start the transfer process now or any time before sep 2019?

please let me know asap.

[scientist2016]

You would be able to apply for cap exemption anytime before 2019. Your next employer would be able to do it if you have a copy of your I797.