Simplistic is if you pay the FPN, that is it, all done and dusted.
If you don't, you (dad) may end up with a summons to magistrates court.... though with the wrong name whether that would stand up is a different matter and IMO likely to provide enough hassle that they would give up..... not a legal viewpoint BTW.
Assuming it did end in court, the authorised agent will be swearing that they saw dad smoking and drop the butt end.
Dad will be saying he wasn't smoking and didn't litter.....
Magistrates decision would come down to whether there is sufficient evidence to find guilty, basically credibility of the two parties.
You come across as credible, can the same be said for Dad...remembering that you were not there and he may have been having a crafty roll up and doesn't want to admit it to you.
Why a authorised agent should pick on Dad and ask if he smoked seems weird.
They do have the powers to demand name and address though cannot force the issue without proper police, who can arrest if needed AFAIK
If it came to court and found guilty, fines and costs would be far higher then the FPN.
As I say, not legal advice as such, just saying as I see it.