This is a really big mess, and it's good that he's getting advice...
If you drum this down to the facts, he is easily linkable to his company (in many ways - nothing on the internet is ever really deleted, so his old association to his employer on Facebook would be findable if you wanted to dig it out, he tagged his employer, Google links him to his employer...) and he has a history of posting offensive political content on social media.
He was warned about Facebook and told to remove the link or stop posting, and he removed the link. Case closed.
He was banned from Twitter, which backs up the companies assertion that whatever he was tweeting was offensive, rather than just a difference of political opinion.
And now he's been reported to his employer for more tweets, albeit fairly mild ones if the worst that he said was calling someone a dickhead.
He is mentally unwell, and is in therapy. He has struggled mentally with the lockdowns, and this was his outlet. He knows he was wrong.
Has this been the case throughout? His Facebook and previous Twitter activity looks like it will have been before lockdown? If he can medically evidence this, it may be taken into account, although it's anyone's guess how much good it'll do.
Yes he is an idiot to have continued his Twitter behaviour when it was clear it was inappropriate. He knows this and has expressed sincere regret and apologised to the company. It will never happen again.
This is what I'd be focusing on. I'd let the rest go in favour of finding a way to convince the company that despite this being his third known offence, he isn't a ticking timebomb waiting for this to happen again. That won't be easy, but if he's genuinely stopped, it's worth a shot.
Has he got another outlet now?
I'd be cautious about suggesting he'll delete social media, but if that's a path he's going down, he could mention that.
He's going to need to show that he is now aware that because of his position, whether that's seniority or an unusual job, he is easily linked to his company; and he needs to behave like that. And he also needs to show that he understands how inappropriate this was.
He may well be able to push to have a final warning, although I'd expect that he'd be a million times out the door if anything like this comes to light again.
But follow the legal advice that he's got, if he's been open and honest with them, because they know you/him/the company/the real contents of the posts, and I'm just going off what you can share here, and a lot of experience doing disciplinaries and appeals for social media behaviour (Joys of a law degree and history working at big social media companies!)