Is the £52k before or after his pension contributions?
He only needs to repay some CB if he's over £50k after pension contributions, assuming he doesn't have P11D benefits like a company car. To check, use the HMRC link above to calculate his 'adjusted net (gross) income' which is what the CB entitlement/payback is based on.
If necessary, he has 2 months to the end of the tax year to increase his pension contributions so he doesn't lose CB, but that could involve giving up a lump sum that you might not have, but if he's likely to continue earning over £50k, it's probably worth planning for this going forward.
On the matter of self assessment, for this tax year (2021/22) he has until the end of January next year to do a self assessment, but he should get it sorted sooner as it can take a while register and set everything up.
But once he's registered, it's really very easy. All you have to do is tell them you're doing the SA to repay CB and they only ask you to complete the relevant screens with a few questions and that's it.
At worst, assuming he can't increase his pension contributions, he'll have to repay 20% of the CB received, so definitely worth a bit of admin to stay on the right side of the law and HMRC and he'll probably be able to repay the excess amount via his tax code.