Alfred Russel Wallace conceived his theory of evolution by natural selection whilst suffering from fever in the village of Dodinga on the Indonesian island of Halmahera (known to Wallace as Gilolo) in February 1858. When he had recovered sufficiently he wrote a detailed essay explaining his idea, which he posted to Charles Darwin together with a covering letter, probably in early March, from the neighbouring island of Ternate. To cut a long story short: when Darwin received the essay in June 1858 he was horrified as he realised that Wallace had independently conceived 'his' theory. He implored his close friend the geologist Charles Lyell for help, and Lyell, botanist Joseph Hooker and Darwin discussed the issue by letter (not face-to-face) and decided to publish Wallace's essay prefixed by some of Darwin's writings on the subject which hadn't been written with publication in mind, in order to demonstrate that Darwin had had the same idea 20 years before Wallace. This 'joint' paper was read to a meeting of the Linnean Society of London on the 1st July 1858, and then published in August of that year. For a detailed account of the curious events which led to its publication see my article Alfred Russel Wallace and natural selection: the real story.
What many people don't realise is that Wallace's original essay and its covering letter mysteriously disappeared long ago. No one knows what Wallace wrote in the letter, and the disappearence of it and the envelope it was posted in have given rise to a conspiracy theory which has been the subject of a number of books and research papers (see e.g. https://onlinelibrary.wiley.com/doi/full/10.1111/j.1095-8312.2011.01858.x). Leaving this intrigue aside, what do we know about the fate of the essay, the letter and the envelope? Well, we know nothing about the fate of the envelope, and all we know about the original essay is that Darwin sent it to Lyell in his 'anguished' letter of June 18 1858 asking for it to be returned. There is no record of what then happened; it could have been sent to the Linnean Society for typesetting and then lost; Lyell could have kept it and sent a transcript to the Linnean Society, then returned the original to Darwin, who subsequently lost or destroyed it etc etc. One thing we do know is that the original was never returned to Wallace (see below).
What Wallace's letter might have looked like - a Photoshop mock-up produced from real Wallace letters by George Beccaloni.
So what became of the letter? All we know is that in a letter of 25 June 1858 Darwin wrote to Lyell "Wallace says nothing about publication, & I enclose his letter." So he sent it to Lyell, who may or may not have kept it. In about 1908 Hooker asked Lyell's nephew to search for any documents relating to this affair among his late uncle's papers. In a speech given by Hooker at the Linnean Society to commemorate the 50th anniversary of the reading of the Darwin-Wallace papers in 1908 he said "There are no letters from Lyell relating to it [i.e. the 'affair'], not even answers to Mr. Darwin's of the 18th, 25th, and 26th June; and Sir Leonard Lyell has at my request very kindly but vainly searched his Uncle's correspondence for any relating to this subject beyond the two above mentioned. There are none of my letters to either Lyell or Darwin, nor other evidence of their having existed beyond the latter's acknowledgment of the receipt of some of them; and, most surprising of all, Mr. Wallace's letter and its enclosure have disappeared." Lyell actually kept four of Darwin's letters related to the affair, the two mentioned above plus two others (see HERE and HERE), but no others. Curiously, none of the letters from Lyell to Hooker are known, although Hooker preserved many of the ones which Darwin sent to him about the matter. As for Darwin, he didn't keep a single letter relating to this matter - or they were later lost or destroyed.
Darwin seems to have replied to Wallace's 'Ternate letter' on 13 July 1858, almost two weeks after his and Wallace's articles had been read to the Linnean Society (see HERE). He enclosed a letter from Hooker which we have Wallace's reply to as Darwin forwarded it to Hooker who kept it. Curiously, although Wallace kept all of the letters he received from Darwin whilst he was in the Malay Archipelago, the key letter from Darwin of 13 July (and the enclosed letter from Hooker) is the only one which seems to be missing. Even stranger, Wallace sent all the letters he had received from Darwin whilst in the 'Malay Archipelago' to Sydney Carlyle Cockerell in 1909 for exhibition at Cambridge