Looking through the biography of Winston Churchill by Roy Jenkins (2001), and reading the part about Churchill's truly unfortunate involvement in trying to prevent the abdication of King Edward VIII, I find a transcript of a strange letter - Jenkins mentions "the rashness of content and the jauntiness of tone, in sharp contrast with the note of measured respect in which he normally addressed his sovereign" - encouraging the king to hold out against pressure to abdicate and naming some potential allies he should enlist.
It's not clear if one of these is intended to be the person named in point 5 of the letter: "For real wit Bernard Shaw's article in to-night's Evening Standard should be read. He is joyous."
I wonder what Shaw said, and indeed whether it had anything to do with the abdication at all - it could have been "oh, you must read this funny article," irrespective of anything else Churchill was saying. I'm still wondering.
There's nothing about this letter in Frances Donaldson's biography of the Duke of Windsor (1975), which I happen to have - the inscription shows it was a high-school graduation present from my aunt - but Donaldson does give context, that Jenkins doesn't discuss, that reveals how futile Churchill's intervention was. By the date of the letter, 5 Dec. 1936, Edward had definitely made up his mind to abdicate, though Donaldson says that Churchill's influence "temporarily weakened the King's resolution." (Churchill came to dinner with the king - Jenkins says the previous day, Donaldson says on both days.) Donaldson even says at one point that the king had already rejected the participation of Lord Beaverbrook, one of Churchill's suggested allies ("He is a tiger to fight. A devoted tiger! Very scarce breed").
But what of Shaw? Donaldson never mentions him; Jenkins says nothing else either. I consulted the monumental biography of Shaw by Michael Holroyd (v. 3 of 4, 1991). All he says of the abdication is that Shaw made "an approving reference" to it in the play he was writing at the time. Holroyd does, however, devote a couple of pages to recounting Shaw's rather peripatetic friendship with Churchill.
If the research libraries were open, I might be able to track down the original article - I doubt there will be microfilms of the Evening Standard (which was one of the papers of Lord Rothermere, another megalomaniac press baron like Beaverbrook), but if there's a collected edition of the complete journalism of Shaw it might be there. But they're not open, so it's moot for now.