Cheers - assuming your partner is the Registered Keeper, with the vehicle's V5C in their name, then they can appeal with the below. If they are not the keeper (the vehicle is a lease car, for example), let us know, as the wording will need to be different.
Dear Sirs,
I have received your Parking Charge Notice (Ref: ________) for vehicle registration mark ____ ___, in which you allege that the driver has incurred a parking charge. I note from your correspondence that you are not seeking to hold me liable as the registered keeper, under Schedule 4 of the Protection of Freedoms Act 2012 ("The Act"). You have chosen not to issue a Notice to Keeper in accordance with The Act, and it is now too late for you to do so.
There is no obligation for me to name the driver and I will not be doing so. I am therefore unable to help you further with this matter, and look forward to your confirmation that the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
If appealing online, be careful there are no drop down/tick boxes that cause you to identify who was driving, and keep a close eye on your spam folder for their response. If they do not respond within 35 days, chase them.
The above has a 100% success rate with Smart Parking so far. As LPS are now part of the same group, I would anticipate the same result.