Missed Furlough Claim Deadline

Throw yourself on the mercy of HMRC, I suppose.

What's the client's excuse ?

And is he aware that the November deadline expires in 13 hours 18 minutes ?

There's a list of example excuses, published 10th December, at
https://www.gov.uk/guidance/claim-for-wages-through-the-coronavirus-job-...

EXTRACT:
If you have missed the claim deadline

For claim periods from 1 November, HMRC may accept late claims if you have:

a reasonable excuse
taken reasonable care to try and claim on time
claimed without delay as soon as you were able to

You may have a reasonable excuse if for example:
[there follows a list of 10 excuses, which I shall leave you to peruse]

Because you're interested in an earlier claim period, scroll down the page to "read previous versions of this guidance in the National Archives" where you'll come firstly across the 19th November version, which has similar provisions relating to earlier claims " HMRC may accept a claim made after the relevant deadline if you had a reasonable excuse for failing to make a claim in time.....

Rolling back to the earlier November updates and the two October updates - which I guess would be more relevant to you - doesn't quite work as you might hope, as you end up (after clicking through "see all updates" followed by "show all updates") on a page which simply logs details of the earlier amendments without directing you to the full archive page. But I believe that list of excuses existed in the October versions.

I do hope there's something you can use from those example excuses.