More often than not there are grounds for appeal. However, without knowing the reasons why your mother, who I presume is the keeper of the vehicle, received the PCN.
Were you the driver? If so, why did you park at the location without a valid permit?
That NtK appears to be compliant with PoFA 2012 which means, if the PPC don’t know your identity and it isn’t provided to them by the keeper, they can pursue the keeper for the charge.
Has the keeper tried Plan A yet? A complaint to the landowner requesting them to get their agent, the PPC, to cancel he PCN?