I've chosen a single paragraph, but one could discuss almost any paragraph with the same results. Original text in bold; my comments follow. I go sentence by sentence without omitting any sentences in this particular paragraph.
After arriving in Bethlehem in 1750, Albrecht established the Boys School and sometime after established a gunshop.
Error (Minor): Albrecht didn't "establish" any boys' school, which was flourishing in Bethlehem for many years before he arrived. He was assigned to the boys' school--probably not until several years after he arrived (we don't know exactly when).
An exact date is not known but according to missionary diaries and other archival records, a gunshop was established between 1750-1751.
Error (Major). No "gunshop" was established in Bethlehem, in 1750-1751 or after. Albrecht arrived and began to work as a gunstocker. He worked alongside the locksmith and all charges (and debits) to him appear on the Locksmith's account. The first "gunshop"--as a separate shop--for Moravians in Pennsylvania was established at Christiansbrunn in August 1763. Bethlehem had in Albrecht a gunstocker--from 1750-59--but it never had a gunshop then or after.
The main gun-making school was to take place in Bethlehem, while the external mission-towns were to have gunshops.
Error (Minor). If the word "school" was omitted, and "gunshops" at the end read "gunsmiths," this would be an accurate sentence. There was no "school" in Bethlehem, just a lone gunstocker without enough work to do and no apprentices. (See below.) Actually, there is a more subtle and important error here. Nobody ever planned to establish "gunshops" at mission stations, though often one of the missionaries had the skills to repair rifles. Big difference between a missionary who could, in a pinch, repair a weapon and a string of "gunshops" at a series of mission towns.
Albrecht's apprentices, mostly drawn from the boys' school, would learn the trade in Bethlehem and once learned would move to serve as journeymen in one of the 5 mission gunshops: Nazareth, Gnadenhutten, Gnadenthal, Friedensthal, Christiansbrunn (aka. Christian Spring).
Error (Major). This is a major misunderstanding. First, Albrecht had (as far as we know) no apprentices at all in Bethlehem. His first apprentice was Christian Oerter in Christiansbrunn after 1759. There was no "school" in Bethlehem (and just a single apprentice in Christiansbrunn during Albrecht's years: not much of a "school"). In Bethlehem Albrecht repaired weapons in the locksmith's shop, and others in this shop must have aided him when he needed more hands than his own. He was not training any young men. He received an apprentice when he moved to Christiansbrunn and could not count on these other hands to help him. Now, even worse: the places the author names here are not "missions." Well, one was: Gnadenhutten, where I think there was a blacksmith who could repair guns. Having such an individual at a mission was crucial; it was the main things the Native Americans requested when they permitted Moravian missionaries to live at Shamokin. None of the other places the author names were missions; they were the small satellite communities that surrounded Bethlehem, populated by white Moravians: Nazareth (a small settlement 8 miles north), Gnadenthal (an even smaller farming community with a few families), Friedensthal (a mill), and Christiansbrunn (at this time, a very small group of single men: only in 1757 would it become a vo-tech of sorts at which masters trained boys in trades). Once Christiansbrunn became a vo-tech, Albrecht moves there and opens the first Moravian gunshop. So, to sum up: Albrecht had no apprentices, no mission towns had "gunshops" (though missions often had a man who could repair metal and iron stuff, including guns), and the places that the author names here (with the exception of Gnadenhutten) were not mission towns at all!!
Albrecht served as Master gunsmith in Bethlehem until 1759, when he moved with the Boys School to Nazareth. It was then that he served as gun-maker at Christiansbunn (Christian Springs) along with his apprentice Christian Oerter until 1766, when he married and took over the Sun Inn (Bethlehem).
Accurate Enough. Albrecht was not a "Master gunsmith," in the sense that he was Master and had apprentices, as I noted above. But the rest of these two last sentences get things right.
The author then includes a photo of a day book ("Tage Buch der Huf-Schmeide in Bethlehem 1753-1754"). He captions this "Bethlehem Gunshop Day Book, 1753-1754, Moravian Church Archives, Bethlehem, PA."
Error (Major). The German title of the daybook says "blacksmith" (literally, hoof-smith) not "gunsmith" or "gunshop." Remember, there is no gunshop in Bethlehem in these years. Now, there is another daybook in the Moravian Archives that has the title "Huff and Waffen-Schmidt" (1753-55), which one would hope would include gunsmith information. This would at least have been a better/more accurate photo to include! But this document, unfortunately, includes no information about a gunsmith's work, let alone work for the "5 mission gunshops" that never existed at places that weren't missions!!
The most generous thing a reader can do is chalk all this up to confusion, rather than a deliberate attempt to mislead. It is hard to be generous with this final item, the photograph and caption, however.
The general import of all these mistakes, misunderstandings, and misrepresentations is to portray Albrecht as the head of a school of gunsmiths who then scattered to populate a series of their own gunshops at mission towns. This is entirely fantasy. It does not correspond to reality. As far as we know--that is, the only information that has been discovered indicates that--Albrecht had a single apprentice, Oerter, during his six years or so at Christiansbrunn. Oerter took over that shop when Albrecht left and Oerter himself never left Christiansbrunn, dying a decade later in 1777.
None of this, of course, bears on what you rightly state is the key question: "what are we to make of the obvious physical connection between these two guns?" But please stop asserting (believing?) that "various ledgers, diaries, letters, and other references ... support the author's contentions." It just isn't so.