Step 1: Gather These Tools and Materials
Knife, puzzle like this one, superglue
Step 2: Leverage
Lever the black bottom off the puzzle with the knife. You may have to lever on all four sides to achieve this.
Step 3: Glueing
Glue one side of the blue thing to the clear box, just under the ridge for the black plate.
Step 4: Stash Your Stuff
The lid should snap on neatly. To open, lever lid off with a knife.