So - on the face of it, if they did not receive the notice, it has not been served, and accordingly, the keeper cannot be liable. However, whilst that is true in theory, in practice, it will be very difficult to prove (how do you prove you didn't receive something?).
Without sight of the original notice, we can't really advise on its contents and whether it is compliant with the relevant legislation - they could send a Subject Access Request to Smart Parking to get a copy of it.
What they do next depends to a certain extent on their attitude to risk...
Option 1 is to pay up - if they do this, there's a 100% chance that they will lose £145. In return for that £145, they will get the certainty that the matter is closed, and the certainty that they won't have to pay any more than that.
Option 2 is to do nothing, await Smart Parking probably taking them to court, and seeking to defend it. If they do this, they might win, or Smart Parking might pull out before a hearing (in either of these cases your friend would pay nothing), or they might lose, which would (generally) cost in the region of £200-230.
On the face of it, from what you have told us so far, they don't have a defence on the basis of the actual contravention, so it would depend on any defencde to be found in the signage, technical defects in the original notice that we haven't yet seen, or Smart Parking's solicitors messing up the process.
I appreciate the above is somewhat vague, but as you can hopefully appreciate, we've not got much to base our advice on currently.