Surely you've got more than this i.e. a description from your dad.
Appointment - so he'll have a works record.
The undated and unaddressed copy letter isn't directly related to this address is it, it's a generic piece of paper which he seems to place in his windscreen whenever he feels he needs to do so. I doubt I'm any more sceptical than the council would be about so why, if he thought he was parking legitimately, would he display this at all, but as he did then he knew he was on a yellow line waiting restriction, yes?
Has this happened before? If do, how did he explain it away?
And on the subject of his company, do you know their view?