If you would like to share a picture of your completed puzzle on Facebook, you can do so at the Game Over screen. After the CONGRATULATIONS! appears, you will see a few large circular buttons towards the bottom of the screen.
Tap the Share button (denoted as 1 in the image below) to share.
You are then presented with several options to share the image.
Select the last option (denoted as 2 in the image below) to save the image to your iPad/iPhone.
You can now access the saved puzzle image in your Photos app.
From here, you can share it using any other app on your iPad/iPhone including Facebook.