The .musx Finale files are just data files. You can drag the folders containing them onto a USB thumb-drive to copy them from one computer and then copy them from the thumb-drive onto your new computer.

Finale files are saved by default in a folder (in documents?) called Finale Files. You can change this in the Finale Preferences to save them elsewhere. In PrintMusic the default folder may have a different name. If you have yourself changed where such files are saved, then you need to drag those files and/or folders onto the thumb-drive.

Very important (though you didn't ask). Be sure to open PrintMusic as Administrator  to de-authorize your copy of PrintMusic on your old machine so you can authorize it on your new machine. It's a lot easier than doing it in retrospect via the Finale web site.

Or, upload the files to Dropbox, One Drive, Google Drive, etc. No thumb drive needed.

If you have any problems with either method outlined above, zip the files on your old drive first, then unzip onto the new computer. 

If you can still log into the old machine, you can also email them to yourself. Email zips and unzips attachments automatically.