It is similar to a relatively common "on the cheap" conversion done in this country and in Europe. It seems to be most common in New England, but it is hard to tell how common they really were since it is not a very durable conversion - the cock will eventually break. Below is a picture of a conversion of this type done to a US M1795 musket:
While some muskets may have been converted for use by various state forces involved in our Civil War, they were not used by the National (Federal or Confederate) Armories.
Below are examples of Swedish military muskets/rifles shared with us by a Forum member from Sweden a year or so ago:
As you can see, all are similar to the conversion shown on the Argentine site, they are not quite the same - the block held in the cock is a little more massive and, especially in the US example, a little cruder. Too bad he only offers the short, so called carbine, but such a conversion could be done by almost anyone on existing reproduction longarms and I have been tempted, but with modern cast parts I doubt that it would last long enough to make it worth the effort.
All that being said, thanks for the link to the site, there is at least one more site from Argentina that offers some very nice reproductions of US, British, Spanish and Argentinian military firearms but I lost the link during a transfer of information from an older computer.