H1 transfer after being laid off

[desi_girl1]

I was FTE for 3+ years for a company , they laid me off and luckily I got temp project on last my grace period ended(on 60th day and I still have my I-94 valid for another 6 months).I received my receipt number but transfer approval is still in process. Mean while , before I get the approval , if I get another job may be another fte , can I initiate my transfer with this new company.

Any help , suggestion is highly appreciated.