This tool works on Fuji Xerox, but neither of yours.
I see no way in CWIS to do so, I tried with the backup option in CWIS>Properties > Services > Print From > Reprint Saved Jobs
but that only backed up the jobs sent from a PC using the Saved Job option in the driver (They do in fact go into a mailbox).
The clone option is available in both devices, but Clones should never be used across device types or different firmware levels (Your case has both) and it would backup the mailbox settings but not the jobs.
Seems you are just plain out of luck. Sorry.