Termination on H1B and 60 Days grace

Dear Sir,

My employer indicated that I will be terminated from the current role a week from now. I had already anticipated this long time ago as the company is small and have used unethical means in the past. I have already received an offer from another company and the lawyers will file the application soon but this will still take 2-3 weeks from now. My lawyer preparing the application for the H1 Transfer indicated that we have to submit the termination letter from the company if we intent to use the 60 days grace. Is that accurate ?