Do as you want, but permit me to note that many of those old guns had their firing pins removed or broken specifically so they COULD NOT be fired. Since you don't plan to shoot the gun (a good policy), I would leave it as is and not fix it. You may recognize the danger but someone coming along later might not and serious injury could result.
The "1813" might be a serial number, but is probably an assembly number, put on to keep fitted parts together during final polishing and finishing.
Jim
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