Carl Fischer (hereafter, "CF") was an importer and reseller. They didn't make any instruments. I'd say that the overwhelming majority of saxophones that CF imported were Evette-Schaeffer, Buffet-Crampon models. I know that CF imported
some Buffet clarinets, as well as several other manufacturers. I also must say that the case looks like an old Buffet case. Of course, you can buy a case separately, so that doesn't necessarily indicate anything.
One comment I read said that CF resold some Pruefer clarinets and some of those had the top joint (read "section") lined with nickel-silver. That's be an easy way to identify! Just look in the joint.
* If you can find a serial number, that'd be helpful. There may be one on each joint of the horn and they may or may not match. The serial number may be fairly faint.
* If you can find a stamp that says, "Made in [Place]," that'd be helpful.
I've also gotta say that the Bundy mouthpiece you have there looks astonishingly like the one I used when I hated playing clarinet and didn't know you could get a different mouthpiece.
On the topic of "restoration," if you have any pins, bands or cracks, that's a sign of, "Probably not."
I should also ask, why are you wanting to get a flute player a clarinet?
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Carl Fischer also imported a lot of
high pitch instruments. High pitch is an older intonation standard. That essentially means that the horn will not play in tune with modern instruments and cannot be made to play in tune. On the CF sax imports I've seen, it's going to have "LP" ("low pitch," the modern intonation standard) or "HP" stamped on it. You might also see "low," "high," "H," or "L."