Furst doesn’t make any references to prior art or work in the historical record except the one which @Graham has mentioned. It appears on p131 of How to Remember as:
This numerical system has been used by Berol, Roth, Loisette and other writers on the subject, and it seems pointless not to avail ourselves of a tested method which has proved satisfactory for many years.
There’s also a reference on page 56 of How to Remember:
Books of modern times dealing with association-laws, for instance those by Loisette and Poehlmann, are divided as follows in respect to the differences in concepts from a purely practical point of view
I’m digging up copies of David M. Roth’s Roth Memory Course, Felix Berol’s Berol System (which may have included work by his brothers William and Max), and Christof Ludwig Poehlmann aka Christopher Louis Pelman about whom I’ve found a nice trove of material on a related method at https://www.ennever.com/histories/history386p.php?sitever=standard. I don’t have much hope that any of these references will credit any of their prior sources as most of them seem to have made their livings on their courses and writing and wouldn’t have wanted to “give away their sources as potential competition”.
There is a chance that Major Beniowski was the source of the system for all of these authors given the relatively wide spread nature of his work during his life, his international travel, and the fact that he spoke multiple languages. But at the same time there’s a large number of people using this or similar methods in the 1800’s. Having more direct evidence would be useful. I only became aware of the moniker by seeing it on the Wikipedia page, and previously used the “number system” as Furst did to describe it.
I do notice that Furst uses the phrase “Furst Method” at least once in his correspondence course, but it’s in reference to the Major System and several other peg and related systems (notably not the method of loci in *You Can Remember*). It seems fairly regular for practitioners of this time period who were writing books to use their surname and call it their method.
One interesting case seems to be that of Marcus Dwight Larrow alias Silas Holmes alias Alphonse Loisette (referenced by Furst) who peddled a system for inordinate sums (including to Mark Twain who gave him a testimonial at the time). His system was exposed in a book in 1888 and was interesting or influential enough to have garnered a book review in the journal Science (see: “Loisette” exposed, together with Loisette’s Complete System of Physiological Memory. By G. S. FELLOWS. New York, The Author. 8‡ 25 cents published 20 July 1888).