I believe a non-JBL Prius comes with 6 speakers while a JBL equipped Prius has 8 speakers. So you cannot just swap a JBL head unit for non-JBL head unit. At least that is my understanding. I saw a post recently where someone installed an aftermarket head unit underneath the existing radio in place of the tray. Something like that may be an option. Good luck. Edited to say I found the thread. Dont know how to add a link yet but the thread title is: Stealth Install an Aftermarket Stereo in Prius
The JBL radio must be paired with the outboard JBL amplifer. In a non-JBL equipped Prius there is no outboard amplifier.....so the short answer is "no", you cannot make a Prius factory JBL radio work in a Prius that does not also have the JBL amp under the seat. There are some fundamental compatibility issues between the two.