H1 transfer while H1 renewal is process and I-94 about to expire

[Akash1234]

I-140 is approved from current employer and my H1B is going to expire on August 30th 2013. My current employer has already filed for H1B renewal under normal processing, reveiced I-797 but waiting for approval, still employed with same company. In the mean while I have received a job offer from another employer, and I would like to know if new employer MUST file H1B renewal prior to expiry (August 30th 2013) of my current H1B or is it ok if they file even after the expiry of my H1B based on my approved I-140. The issue is it may take some time for the new employer to file H1 transfer/extension due to internal approvals etc.

 

Please advise.