It’s the registered keeper’s responsibility to pay it, not the driver. That’s how council penalties work.
By all means, pay it and get the money from them. But don’t just hand the letter to them and say “here, you pay this”. Because if they don’t pay it, it’s you the council will come after.
There’s a 28 day limit for serving a penalty charge notice. I think it’s 28 days to you receiving it, not 28 days to them posting it. Happy to be corrected on that.
Usually when this happens, it’s because the council took 27 days to print and post it. Those ones can be cancelled fairly easily. That’s not the case here - the council printed it fairly quickly and the post took forever. It’s hard to prove that.
You can send an appeal to the council and ask them to re-offer the discount. Most will, but some play hardball with postal PCNs and don’t re-offer it. It’s worth a try - you’ve got nothing to lose.