This subject comes up endlessly... it seems that every commercial light musket is an "officers' fuzee". In fact, real officers' muskets are quite rare. They enjoyed a reasonably brief popularity in the British army, from the Seven Years War through the American Revolution and, to a lesser extent, perhaps into the 1790s. They were a reaction to fighting in North America where the traditional spontoon was particularly ineffective and, in wooded terrain, positively a menace. They were never regulation arms but were tolerated because they were a practical arm for use in the field. One of the great ironies of collecting is the miss-identification of so many commercial arms as officers' muskets has created the impression they were more common than they really are.
In British service, all of them were privately purchased. Their quality reflects the social standing of an officer who was someone who had to have a private income. This was true of militia officers as well where there were income qualifications to assure that the commissioned ranks would be filled with "gentlemen."
The fuzee was the field arm of company grade officers of infantry. Above the rank of Captain, all officers served mounted, a situation where a musket was useless. I have been collecting copies of portraits of British officers with fuzees for a good 30 years... virtually all date between 1755 and 1795. I've yet to find one as late as 1800 but don't rule out that possibility. I'm attaching some photos of my most recent acquisition. This one is by David Blair, a Birmingham maker who died in 1815. I have not run down his actual working dates but I suspect it dates from about 1780. Notice that it has a bayonet lug, was fitted for a sling and has steel mounts. Steel mounts were often as expensive as silver mounts and would be appropriate for an officer of a regiment that wore silver buttons. Brass mounts are also seen. Despite several publish attributions, I am skeptical of silver mounts unless all of the other salient features are present - the sling and the bayonet lug. Silver just isn't a good choice for field use but it may be the sort of thing a militia officer who was aping the style of the field army (but had little reason to expect field service) might purchase.
Well, I tried uploading the images. No luck... and I'm not wasting my evening trying to figure out how yet another system works.