Currently your partner has the PCN as it was issued to the RK. If they were not the driver, then it will only be the driver if they throw them under the bus.... Best to edit your post to refer to 'the driver' rather than I.
The RK needs to send a Data Rectification Notice to Premier Parking giving the current address as address for service, and instructing them to erase any old address, and the inform any third party (eg DRP) about the change. Failing to do this means that if they move to small claims court the RK as defendant may not hear about it, and they will get a default judgement. At the same time, the RK can submit a complaint that they didn't receive the PCN and request that a copy is sent. Once you have this, then it can be reviewed for compliance with legislation to transfer liability to the keeper. Any appeal based on the actual event is likely to rebuffed, but if they have made a mess of the PCN, an appeal on this basis might have more traction. Make sure the RK(*) communicates only as RK, and the driver is not identified.
* you can do the leg work, but it needs to be in the name of the RK.
The RK also needs to get the registered address for the car updated with DVLA!
