Hi Bill
The gun you posted is typically called a Belgium "Trade" gun for a lack of a better term. The one you have with the 51" barrel was probably made in the 1960's and marketed here in the U.S. by a couple of companies, Century Arms being one of them. They called your gun the "Long Tom" LOL. You will probably find the stock on your's is a two-piece affair, with the rear barrel band covering up the divide. You're lucky your gun has the one piece lock plate which probably utilizes a long v-type mainspring. Others were made with a two-piece lock plate affair utilizing a coil mainspring that worked, but was less attractive. I owned one of these. Frizzen had to be re-hardened. Guess they started running out of the surplus one-piece lock plates (?)
The one-piece lock plate dates to the 1950's and earlier. The earlier ones, dating back to the turn of the 20th Century, were of higher quality and as mentioned were originally intended for the natives in the South African market. Occasionally, one of these earlier ones comes up for sale.
Apparently, sometime during the 1960's the shop(s) in Belgium making these guns must have determined there was a better market in the USA. Possibly with America's approaching Bicentennial. And likely the reason for the eagle stamped on your lock plate. But I do remember seeing ads in gun magazines back then for your exact gun. They had at least three different models sold here in the 60's. One was 4 gauge that Dixie sold back then called an "Elephant Gun". There was not much variety of shootable, replica muskets available in the 60's like there was starting in the 1970's. I had one of the two-piece lock in the standard model I bought in 1964 I believe. Paid $35.00 for it plus shipping. Your "Long Tom" was like $5.00 more, but didn't come out till a year later.
Belgium has a long history, going back to at least the latter half of the 19th Century of buying up old surplus gun parts from governments, etc. and building inexpensive guns for the general public utilizing a combination of new and surplus parts. That's why many of the muzzle loading guns are often hard to identify their origins. They were often made later than they would first appear.
Rick