He has to tell them because the car belongs to them, it's their asset on which the finance is secured against. Their exposure and risk is now increased as they've no asset to repossess in the event he stops paying it. Not that I'm saying he will, but that's the way it's looked at. Ultimately, it's not his car, it's theirs until the finance is cleared, and they need to be made aware of what's happened to their vehicle. Things may have changed as I don't work in that specific area anymore, but as soon as the car is officially written off - its highly likely they'll be aware anyway. Not telling his insurance isn't great for him either.
Speak to them, in the age of treating customers fairly, they won't negatively impact his credit file unless he puts them in the position to do so. They may offer to reduce the balance, but this is generally when he pays them the scrap value of the car as a partial settlement towards his agreement. If he was planning on overpaying anyway, the partial settlement plus the overpayments would save him overall on the interest on the agreement. That won't impact his credit file.
If he chose to go down the route of making a reduced monthly payment (for instance, if he needed to do so to finance a new car and he's not in a position to pay two finance agreements) that may just be marked on his credit file as an arrangement, but still show as being paid on time. It has marginal impact on his file at that point, certainly not enough to prevent him financing again - unless his credit file is poor already - but in general it doesn't have as big an impact as people think it will.
Another option could be to speak to them and ask how much negative equity they'll allow him to carry into a new agreement. Could be an option if he needs to refinance. They would then reduce the amount he owes now, in way of the remainder of the terms interest being rebated. Caveat to that is, he's rolling that into a new car and therefore paying more overall for that one - and that's where it's especially important he considers fully comp insurance. Say his balance outstanding now is 10k, his settlement figure is 7k, he buys a new car for 10k, but his loan would be for 17k. Unless we're talking reasonably small figures, it wouldn't be a great idea to do this unless he's looking at 2/3k of the current agreement being carried over.
His finance company will be able to talk through all of his options and as long as he meets his payments, they won't force him into an immediate decision. They have a responsibility to be fair and transparent, and put him and his financial wellbeing first.