Change of status from L-1A to H-1B

[cheers@1]

I wanted to check if there is a possibility of changing status from L-1A to H-1B without going thought the CAP if I had a H-1B before. Below are details of my situation.

Worked for Company A from Sep 2002 to Mar 2011
Company A filed for H1-B in 2004. Below is the duration spend in the US
Travel through H1(total 5.5 years)
Nov-2004 - Mar-2005
Feb-2006 - Nov-2008
Dec-2008 - Mar-2011

Resigned from company A in Mar 2011 and joined company B in India.
Renewed Passport in July 2011
Company B filed L-1A in Aug 2013.
Oct-2013 - Present

At this stage, If I want to move to another employer, do they need to apply for a fresh H-1B or can the old one be renewed / transferred. Please advise.
P.S. Assume that GC via E-B1 is not an option.

Thanks.