Albinoni's biographer, Remo Giasotto claimed to have found a six-measure fragment from a lost Trio Sonata, and supposedly constructed the Adagio in G minor. More recently, Giasotto confessed to the hoax that it had all been made up, and was a completely new 20th Century neo-Baroque piece.
According to Wikipedia, Giasotto purportedly constructed the balance of the complete single-movement work based on this fragmentary theme. He copyrighted it and published it in 1958 under a title which, translated into English, reads "Adagio in G Minor for Strings and Organ, on Two Thematic Ideas and on a Figured Bass by Tomaso Albinoni". Giasotto never produced the manuscript fragment, and no official record has been found of its presence in the collection of the Saxon State Library.