If your practice has the Whiteboards feature (read more about this here), you can move the patient from whiteboard to whiteboard easily!  

On the iPad:

In Editing mode of the patient's flow sheet, tap "Edit Info":

Then tap on the whiteboard the patient is currently in (ie Emergency) and choose the department's whiteboard you wish to transfer them to and tap "Done":

The patient will now show up on the new department's whiteboard!

You can view a video of this feature here: