This is sphaero2, a derivative of the original sphaero Jigsaw Puzzle application by Paul Brinkley:
I've kept the heart largely unchanged - the general cutting of pieces, the main puzzle class, and the basic image handling and display. It's been refactored a bit, modernized (so it needs Java 5 or later), cleaned up, and the user interface has been tarted up significantly. To be honest, the basic core was pretty darned good already, the interface just deserved a little extra TLC.
The name I've used is sphaero2, to make it clear that it's a derivative of the original sphaero, but isn't quite the same.
There is no explicit license on the files, but the sourceforge project page says GPL, so I'm assuming that's what the license is. (Except for ImagePreview.java, which is copyrighted by Oracle.)