Viewer asks how was that kuchen
wrapped, tucked into the laundry case among the clean clothes and mailed back to the dorm? You're right, it certainly wasn't in a plastic bag. Nor was there aluminum foil -- I don't remember ever seeing that before The War except on chocolate bars. Neither aluminum nor the more familiar tinfoil would have been available in the kitchen anyhow, when all metals were needed for the frantic manufacturing push to defeat Germany. In those days if you dropped a single bobby pin or hairpin you spent however long it took to find it.
Saran wrap hadn't been invented yet (years later you will recall Benjamin Braddock being advised that the coming thing was Plastics.) Cellophane was still so new that Cole Porter cited it along with the Eiffel Tower as wonders that were The Tops!-- and anyhow, it was available only for commercial products.
Mother wrapped the kuchen in waxed paper, a/k/a wax paper. She didn't need to put it in a box. That sturdy laundry case was perfectly designed to take the slings and arrows of the postal service -- which, wartime labor shortage notwithstanding, still gave us two mail deliveries a day.