H1B Transfer - Letting Former Employer Know for Termination

Dear All,
I will really really appreciate if I could get a response to my 2 queries related to H1B transfer mentioned below:

1) My employer is a staffing company A. I am currently on bench without any job on hand but according to my agreement with my employer,I am being paid on bench. My current employer has generated my payroll until April 1,2011.My pay-on-bench agreement with my employer A has already ended with this last paystub on April 1,2011.I have a job offer on hand from Company B and they have started my H1B transfer under premium processing with 3 paystubs with latest paystub being April 1,2011.I am very sure my visa transfer will get approved.Now my question is how soon do I need to let staffing company A know that they can cancel my H1B as I have already found a job?What if I don't let staffing company A know at all that I have started another job as anyways they won't be generating my new paystub?

2) Is it mandatory on my side to let my former employer A know that I have started a new job so that they can revoke my H1B?

3)Considering my new job starts on May 1,will this 1 month gap from April 1 to May 1,2011 affect my GC filing after 1 year from now?

Many many thanks in advance for the replies!!

Why do you want your former employer to cancel your H1B? You can simply resign. For that matter, from what you've told us you've already been laid off.

Your employer does not have to revoke your employment authorization.

I'm not going to speculate as to whether a month of unemployment, and hence being out of status, will affect your application for LPR status. Discuss the details with an immigration lawyer.