You'll need to change the SSID in which the Pronto TSU-9600(9400 or 9800) sees. As stated above the RFX-9600(9400) does not need to be pointed to a new SSID. As they are plugged into the new router via the Ethernet cable.

In Pronto Edit, while working on the file that is downloaded into the Pronto TSU-9X00 unit. You'll have to look at the Network tab. Under there you'll see where the SSID and passcode is entered. This can be under the Master Project area or the Device Project area. It all depends on your setup.

I recommend saving the original file by itself and make a copy of the new file just in case something goes wrong.

KOT