I had this potential scenario and I was very relieved that my relocation didn't materialize. This will inevitably delay your case and if you have any option (e.g. commute to your new location for a few months and keep you residence where you are now) I would advise not moving during this stage.
If you go ahead with moving, you will need to contact the National Customer Service Center at 1 (800) 375-5283.
Your case will be transferred to your new Service Center & District Office. My understanding is you will have to wait 3 months after establishing residence in your new state / district before you can expect anything to happen.
Remember, you are also required to submit an AR-11 (IN ADDITION to calling the 1-800 number) to report your change of address -- this is because your are still a PR, and has nothing to do with your naturalization.
