My boyfriend had some left-over foam plastic which hasn't yet found its way into the dustbin but fitted nearly perfectly into the compartments.
I cut them with a hot wire cutter to the preferred size and with a cutter slices into it - don't cut too deep, you still want it in one piece! You should cut the block a bit smaller because you need some space for the fabric.
Then you take a nice fabric with is not too slippery and not too thick (no satin, no home linen; I used the remains of a dress of fine wool). Cut it in a long strip, you need to wrap it around on all sides. Don't cut the forth side yet because it takes more fabric than you think!
Now put the fabric into one to the next slit, I always begin on one side and move to the opposite.
If you have problems with keeping the fabric where it should be you can use sewing pins to keep it in place before you put it into the box. Just make sure the pins are not where your slits are!
You can also use a double sided tape to fix the foam parts on the bottom of the box.
To keep it open by itself I attached a ribbon with two nails.
This works with every box!