What key and why does this work?

[jancivil]

but the first part of the sentence (what key?) in the OP can't really be answered. We'd almost surely need more music (before it or following it).

... which likely won't happen. This was the OP's first & last post ever.

I'd wager you're right about that. But while seeming to beat a dead horse I hope an object hint about how to get a real answer from people may be had there.

This doesn't have a sense of even being a whole musical sentence, frankly.

[Scoops]

Could be Cminor where the F# chord is a tritone substitution, and it resolves with a picardy 3rd on the CM chord.

The possibilities are limitless

[jancivil]

If it's Gb - Fb instead, it could be looked at as a secondary dominant: V7 of Cb. Or b5 substitute for dominant, bII7 *of F.

Picardy Third means the end of the piece. That is not in evidence. It seems clear enough it begins in or in vicinity of C minor and the end of the progression is a C major harmony. We aren't ever going to hear it apparently, it may just be a naive effort with no attention to voice-leading.