Hello Vlad 
,
Can you print the container number on the print out stuck to the box ?
Then you can correlate it with the container shown as red (empty) in PK13N.
And this way the material handler also knows which box corresponds to which container. You could also make a change in the purchase order / production order print to indicate the container number for which it is generated.
I am not sure if you have explored this possibility.
Else the other way is to use enhancement, and find out which container is empty starting from container 1.
Hope this helps.
Best Regards,
Ameya B.