Was this a Thameslink train? This is pretty bad luck because the
rear portion of 1st class on Thameslink trains is open to use by Standard Class ticket holders, so if you at least had a standard class ticket - you could have gone in the rear 1st class area to charge your phone and that would have been totally legitimate!
Off topic but the reason the standard class areas on Thameslink have no charging points is that the UK government, when they specified the trains, specified them without passneger charging facilities / sockets throughout the train to save money - unbelievably poor!
Anyway - back on topic - if this is Govia Thameslink Railway (GTR) they are fairly pragmatic - and if you contact them urgently - may be prepared to settle the matter and withdraw court action process.
You need to write and explain the whole issue has only just come to your attention (which it has thanks to the unhelpful actions of your family member who must have opened the earlier correspondence, not understood the seriousness of it, and shoved it in a drawer...), but that you would not like to resolve the matter as quickly as possible without the need for it to be handled in court.
Adopt an apologetic but co-operative tone, making clear you are happy to pay sums owed*, and this might work. It will likely cost more than if you had resolved matters at the time but of course that chance has now gone by
You could post a draft of what you want to write to them up here for people to check if you think that would help.
keep copies of all the paperwork, send stuff signed for so you know it has got there, ensure relevant ref numbers on whatever you send etc
Hope this helps - others might post good advice so keep an eye on your thread here for eg next day or so
In all of this I am assuming that there is enough time before the court action for you to open this dialogue with GTR?
Then if they agree that and you can get confirmation in writing that the court action is withdrawn I assume there would be no need to notify your employer and that resolves that aspect for you.
Also - prev threads involving Thameslink where people have engaged lawyers have mentioned one or two forms who seem to have a sting relationship with them which means they can get settlements done quickly - but of course that comes at the cost of the solicitors fees. I suspect you don't need that help but if you do the firms names can be mentioned here if that would help / or if you wanted to get a quote - I have no connection with them nor have used them myself I should add
This thread is an example (far more serious problem than yours -
https://www.railforums.co.uk/threads/fare-evasion-thameslink-gtr.255532/#post-6441151
*
EDIT - hopefully no more than the sums mentioned in your uploaded docs ie £150 costs + £19.20 fare (I see you indeed did have a standard class ticket)
My advice for next trip on Thameslink - use the rear 1st class area with a Standard Class ticket - tables, charging points and slightly better seats
(ceiling mounted screen in that area usually says as it scrolls thru various messages that Std Class ticket holders can sit there)