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There's a button there that allows you to automatically complete a puzzle if it's done. Only now, after the update, it doesn't work yet. But when it does, you can put the pieces back in place with one click.

OK. But if I go to the puzzle, just to look at it, it is blank space with all of the pieces floating in the pool.
Which is sort of annoying, because it is a nice image to view complete

the purple piece in the bottom right corner is a sign of completion. So it's okay.