That the library window remember is position???

That the frame sizes(tiny, small) are saved?????

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It's not that easy to pull off as unlike all other panels, there's one
library for each FLA, it means if you open 10 FLA-s you can open 10 Library
panels.
Don't get pissed about little hassles, but simply hit CTRL+L and put your
panel where you want and do the job ;)

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Hm that's weird it won't indeed, I agree this needs to be addressed... but
don't tell me this ruined your day ;)