Your firearm was a Muster 1844 Kammerbüchse. The "patch box" was actually a tool box for the soldier's small gun tools which was installed on the rifles from 1844 to approximately 1847. The Austrian Army stopped putting them on the rifles at that point. It may have been an economy measure, it may have been because the tools rattled in the box [not a good thing for Jägers when they were on the fire [skirmish] line], or it may have been because the box lids came off and were lost. The boxes are rarely seen on Muster 1844 Kammerbüchse in the United States. I don't know if it was because only small numbers of the variant were imported or if the survival rate of the variant was very small during and after the war. The numbers that you show in your photos are manufacturer's or assembly markings, and not even the Austrian Army Museum has a crib sheet for them. Most of the rifles were produced by contractors, particularly Ferdinand Früwirth, and the manufacturer's name should be on the top of the breech, although it may have been obliterated when the rifle was transformed to percussion. Any Austrian unit markings would be on the left breech of the barrel forward of the chamber [Kammer] section, on the top of the buttplate, or just below the head of the ramrod. The 'lump-of-metal" transformation to percussion is of Piedmontese Army design and was made after the rifle left Austrian service in the Kingdom of Piedmont-Sardinia [possibly] or in Liege, Belgium. The Belgians did not proof the weapons after transformation so there are no Belgian proof marks.
Regards,
Don Dixon