60 grace period period clarification please help

[ansari10]

I am on H1B 9th year valid until Nov 2019, with I-140 approved in December 2014. My current assignment  ended on 9/29 at client location 1 , my current company A is trying for other location for next assignment , company has set up the  end date 10/25 to relocate to India if i do not get anything on next few days.I am at home using sick leave and vacation leave available to me. At the same time, i got an offer from new employer B with the same client location 1, they are working on my offer letter but slow on process, then other steps to be followed -acceptance, submission of documents, LCA and filling transfer. As 10/25 is reaching soon, I may not get the receipt number of H1B transfer by that time.

a) Can I resign current company A on around 10/23 even if I do not get the receipt number considering they will process the resignation on next  day or two as i am out of assignment anyway ?

b) Can I use the 60 day grace period after my resignation date, and wait for receipt number to join new employer B?

Please help.