How do I pack this into my luggage?

I’m bringing home some jigsaw puzzle from overseas and I want to put them in my check in luggage.

I really don’t want the boxes to get crushed in transit. The puzzles are already finished and flat in the box. I was thinking that if I put clothes in there until the boxes are full then they probably shouldn’t get particularly damaged from the average jostling between destinations.

Is there a better way of doing this?