Hello,
You could implement this archival functionality using standard configuration:
1. Create a custom report based on the processed messages query (you could also duplicate/enhance the query itself for more information)
2. Create a new Scheduled Task - Report Execution Task and configure it as Integration Export with the report provided above.
3. Set the task to run every 7 days and configure to push the files to an FTP server with timestamp and you'll have a full log of the processed messages.
Regards,
Bogdan