http://h1base.com/page.asp?id=144
(I do not know whether the information on this web site is accurate, but it may help you with some H1-B questions. I also do not know what you meant by H1-B "transfer" - to me the national lab would simply be filing for your H1-B as your university did. The only difference may be that this time your application will not be subject to quota, as this would be a "replacement." Correct me if I am wrong.)
According to the regulations, if the H1b Visa holder (alien) is to perform services for more than one employer, each employer must file a separate petition with the Service Center having jurisdiction over the area where the alien will perform services or receive training, unless an established agent files the petition. In spite of the Department of Labor’s earlier pronouncement that different employing entities could be treated as joint employers, the INS has stated that it does not recognize the concept of “co-employers” in employee leasing agreements.
When employers share responsibilities for the employee, one of the firms must designate itself as the employer, or, if the alien has two employers, each must file a petition.
The INS has consistently stated that neither the new employer nor the beneficiary need take action with the INS if the beneficiary switches employers, as long as multiple petitions were approved and the petition for the current employer remains valid.
For example, where an alien had two petitions approved on his or her behalf, elected to take up employment with Employer A, but later became dissatisfied and switched to Employer B, no new or amended petition was required. Similarly, the Service has advised that, presuming both employers have petitions approved, an alien could take a 6-8 month leave of absence from Employer A to work for Employer B, and then resume working for Employer A without filing a new H1B visa petition. Nor was a new petition required when the beneficiary had switched back and forth between a parent company and its subsidiary, where both had approved H1B petitions.