I completely stand on the side of your university lawyer. However, many company lawyers say such a transfer is unaviable probably just for safety of their job. Your siutation is differnt, you already own a quota. The law says
`(7) Any alien who has already been counted, within the 6 years prior to the approval of a petition described in subsection (c), toward the numerical limitations of paragraph (1)(A) shall not again be counted toward those limitations unless the alien would be eligible for a full 6 years of authorized admission at the time the petition is filed. Where multiple petitions are approved for 1 alien, that alien shall be counted only once.'.
An AILA FAQ says
2. Is someone who obtained H-1B status three years ago, but has not been maintaining status for the past year, still subject to the quota?
If the individual was in the U.S. during all or part of that year, s/he is not subject to the quota, since AC21 section 103 amends INA section 214(g)(7) to make clear that anyone who already has been counted in the past six years would not be counted again unless eligible for another full six years. However, if the individual had spent that one year outside the U.S., under INS regulations s/he is eligible for another 6 years of H-1B status, and thus would be counted.