Once connected to your AS2Box.net Web Folder, you will have access to the following folder structure:
/incoming [Read & Delete]
The messages you receive from your trading partner will be written in both /incoming and /incoming/archive. You will be able to move the files from /incoming, but all the files will remain within /incoming/archive.
If you want to send a file to your trading partner, you just need to copy it to /outgoing, it will then be picked up, save within /outgoing/archive and send to your trading partner. The MDN will then appear in /outgoing/archive next to the copy of the sent file.
Could it be simpler?