Whether you've accidentally added a case to the wrong program or they are switching to a new program, you will first need to discharge the case.
Click here for instructions on how to discharge a case.
Once discharged, go to the case and click on the Reopen button and select "Readmit (New Case)".
A pop-up will then appear asking for additional information, fill out all fields highlighted in yellow then press OK. This pop-up is where you can change the program the case is assigned to. Make sure you have your pop-up blocker disabled for extendedReach!