Nice headstamp! Based on German 9mmP boxes I have seen from WWII era, the box impressed on the cardboard box probably doesn’t have much baring on the date of the ammunition. the German and occupation P08 boxes in my collection have impressed stamps indicating the date the box was manufactured. Some are years earlier than the label. Clearly boxes were reused ince there are many incidents of multiple labels. The bottom label is not infrequently a proof label so the the ammunition was probably used in a gun factory or some other facility and then recycled. Other boxes have only a single label but it is years after the box was made. These could have been boxes that spent years in storage before use, or boxes which were not labeled when originally used (perhaps for some use inside the ammunition factory).
I know this data relates to German, not Hungarian production, but my guess is the 'Allies" used very similar processes. The cartridge cases were apparently produced in 1944. It appears that the 1939 box was either reused for this ammunition or stayed in storage a long time before use.