Is my H1B change of employer petition cap exempt?

My visa will expire on July 31, 2012. I got a new employer and will file for my visa extension. I have used 4 years out of 6 years in my H1B.

My lawyer told me we have a problem because when my H1b petitions were filed in 2008 and 2009, it was filed as cap exempt. I worked in a school district and will be transfering to another school disrict.

Based on your question I am assuming your new employer is not cap exempt

1) In such a scenario you H1b transfer would be cap subject. The rule states that  If you were already counted in the cap within the last 6 years, you can file for an H1B to continue as cap-subject for the remaining time allowed under an H1B, which in your case does not hold. 

2) Since the cap subject quota for this year is over, it would be better for you to continue with the current employer till the next cycle, also remember that when you file for your cap subject transfer  you would only be eligible to start working from Oct 1 except under certain special circumstances

The school that will sponsor my visa extension has not done visa sponsorship before. This is the first time they are going to do this. Can they explore a way to be cap exempt?

Most universities and non profit organizations are cap exempt. An organization is either recognized as cap exempt or cap subject, and there is no go around for this. Since its School check with their administration/attorney to see if they are cap exempt.

Also it might be helpful for someone else who wants to chip in if you can clearly mention the status of both your employers and provide any additional info you can share .

My lawyer and the school board will discuss on Monday if the school is cap exempt. This is their first time to sponsor. My previous employer is cap exempt because it is university affiliated. My h1b visa is expiring on July 31, 2012. My new employer is also a school but not sure if it is cap exempt.