Well, I can tell you a "dirty hack" that will allow you to download all messages from your Exchange server. However, it's not recommended solution, because it is not an official feature.

To do this hack you need to:
1) Connect your device to PC in mass storage mode.
2) Open /home/user/.accounts/accounts.db (it is an SQLite database, so you need something like sqlitebrowser to open and edit it)
3) In this DB you should find in "settings" table an "email/past_time" setting (this is a string in the 'key' column) for your MfE account and change value to 0.
4) Save DB.
5) Disconnect your device from PC.
6) Reboot the device.
7) Sync your MfE account (if it will not start syncing automatically).

WARNINGS:
1) This hack might confuse you a bit, because after that hack you will see sync back mails as "3 days" value (plus it might overwrite this setting in the DB, so it's better to not save it at all (or even not open mail account settings)).
2) Manual changes in the accounts DB might corrupt the DB, so, in case of any troubles, you'll have to recreate ALL accounts (this is means that you will lose ALL accounts info).
!!!!THIS IS NOT SOMETHING RECOMMENDED TO DO. DO IT IF YOU KNOW WHAT YOU ARE DOING. DO IT ON YOUR OWN RISK - All the accounts can be corrupted!!!!!!!