This functionality is designed to be used in the rare cases where a daycare pet is not picked up. (They are unexpectedly required to stay the night.)
To access the Move Daycare to Boarding option begin in the PetExec menu Daycare & Boarding-->Move Daycare to boarding.
All pets currently signed into daycare will be listed here. For the pet you would like to move follow these steps:
The pet(s) moved will then appear on your boarding dashboard. You can click on the appropriate "edit boarding" button to modify the boarding.