L1 B to H1 Cap Exempt conversion (Universities)

Hi,

I am on L1 B, and never had H1 B, and was not through the cap for this year. I work for University, and is it possible to have H1 B Cap Exempt through University, as this is IT job, would be they be eligible, if they want to process.

Please let me know,

Regards,

Sri

Higher education institutions (includes Universities) are eligible for cap-exempt petition filing.