If an H-1B scholar wants to change from another employer to employment at Ohio State, a new H-1B petition must be submitted to USCIS before the employee can start working at Ohio State. USCIS portability regulations allow the individual to start working at the new employer when the USCIS official receipt notice is received and it is on or after the requested start date of the H-1B petition.
USCIS has established a new grace period that allows 60 consecutive days, or until the existing validity period ends, whichever is shorter, whenever employment ends in order to transition to new employment in the United States. An individual may not work during the grace period and the grace period may only apply one time per authorized non-immigrant validity period. Arrangements should be made with the former employer and Ohio State to accommodate the move. The portability petition takes 4-7 months.
See Step by Step for more details.