] I've seen a few references to a letter George Austen wrote to young Francis in 1788. when the lad had finished his training at the Royal Navy Academy and was about to set out on his first tour of duty (the article linked in JA's politics quotes a few lines). Francis apparently kept it all his life. Is the whole text available anywhere? Preferably on-line.

I found it in print, in (where else but my recent favorite JA book!) Jane Austen and the Navy by Brian Southam pp. 29-31. There is also an appendix with comments on the religious aspects of the letter, or 'Memorandum' on pp. 315-16.
Oddly enough, I can't find out where Southam's copy of the letter comes from, but I would bet it's in one of the Austen family memoirs or another JA biography.