The top image is of all four pieces prior to assembly.
The second is an assembly pic with the teal leather and the magnet in the middle.
I used simple wood glue to put it all together and it is quite strong.
One unfortunate issue I have found I need to be mindful of with engraving leather. If you are working with light colored leather and your intent is for the engrave to remain dark, you have to seal the leather before doing much with it. Otherwise, the black soot rubs off and not only do you lose the darkness of the engrave, it smudges the light leather.
The artwork is not mine. I pulled it down from www.graphicsfactory.com, then cleaned it up in Inkscape and created the rest of the piece.