Am I exempt from H-1B cap?

[visaonlinenew]

I was working with Company A in India and they filed H-1B petition for me in 2007. I got the petition approved and stamped the visa after some months. But due to project requirement changes , I was not required to travel.

I continued to work for Company A and in 2010 they applied L-1B for me.Right now I am in USA with my L-1B visa.

Now Company B offered me a Job, So I told them I need H-1B sponsorship and can start only in Oct 1st, 2012.

My Question is since I had one H1-B approved petition (visa) , is there a way I am exempt from the cap.Even though I did not use that visa to travel.

Thanks

[kabkaba]

Yes, they can file a cap-exempt petition and request immediate start date.

[visaonlinenew]

Thanks for the response. Can you confirm this by looking at below details. Also tell me till when can I get H-1B cap exemption--any 6 year rule or anything? I would like to know till when I can apply H-1B without cap limit?

1) H1-B petition date was May 2006 (2007 Quota)

2) Visa Stamped Date was Mar 2008

3) Never Traveled on the Visa even once.

40 H1-B expire date was May 2009

4) H-1B cancelled when I applied L1-B

Yes, they can file a cap-exempt petition and request immediate start date.

[kabkaba]

Cap exempt petition must be filed within 6 years of the previous petition. Your new employer's attorneys will know how to handle it.