Your responsible officer will sign the release only if the transfer clearly is for the purpose of completing the original objective, if it is consistent with the goals of the exchange visitor program, and if your sponsoring UIUC department agrees. The IAP-66 is returned to that officer who will have you complete the form and give you the pink copy. Transferring does not extend the time limit for your category. It is virtually impossible to obtain approval to change your J-1 category in the U.S., because it usually represents a change of objective. In most cases it would be most expedient to apply for a change to another relevant visa status if you are qualified or to leave the U.S. and reenter in the new J-1 category or a new status if the circumstances allow.
Participation refers to physical presence in the U.S. including the grace period.
This regulation applies to J-2 dependents as well.