Even if he pays up - unless he does it within 28 days of the CCJ being granted - the CCJ will stay on his CRA records for 6 years, but should be marked as satisfied. His only chance of getting it removed entirely is to ask the Court to set the judgement aside on the grounds that he was not notified of it. However, the Court is only likely to do this if there is realistic evidence that - on re-hearing the case (which is what will happen after a set aside) - the decision would be likely to be different.
What did he actually do? Did he send DVLA the relevant part of the log book? Did he contact them again when they asked for the money? If he didn't do these things then he probably hasn't much chance of getting a set aside. If he wants to pursue it he ought to talk to DVLA and ask them to confirm what information they have on their records about it.
If he doesn't succeed in getting a set aside and different decision, he will have to pay the money.