Go to your schedule maker (PRO) and expand the Settings section
if you're not on PRO, just ask us to do it for you
Click Edit Selected above the League / Tournament Series dropdown

On the resulting popup, select the organization into which you want to move the schedule and submit the form:
Teams, Players, Venues, Division are all automatically added or moved (if they're not used in any other leagues in the original organization) to the new organization.