The foreign national is eligible to work until the petition is adjudicated. Once the H-1B petition is approved, this “interim” authorization to work ceases, and one of two things can happen. One, USCIS will use its discretion and approve an extension of status and the employee will continue to be able to work for the new sponsoring employer. Or, two, USCIS will deny the extension of status request and the employee will have to depart the U.S., and either obtain an H-1B visa at a U.S. consulate, or, if she already has a valid H-1B visa from her former employer, she will simply need to depart the U.S. and, upon re-entry, present her old visa with the new I-797 and continue working.