Restoring Backup to New Axim

I believe this method will work:

Make a backup of your existing Axim using ActiveSync on the desktop. It's slow but reliable. Backups created by Dell's Data Backup utility have failed to restore as reported by a number of people in this forum.
Remove your old Axim from the cradle and put the new one in.
When the Partnership Wizard prompts you to create a new partnership, click Cancel. You will now be connected via a Guest Partnership.
Use ActiveSync to restore.
When the restore completes, you should get prompted to remove your Ax from the cradle and soft reset. When you put it back in the cradle, your Ax should be recognized under the existing partnership.
Do not connect your old Axim for syncing after a successful restore to your new one.

The backup utility included on your Dell Handheld will backup your data to a storage card. You can restore on your replacement handheld from that storage card.

From your Host PC, you can go to Tools | Backup/Restore and do a backup to the Host PC, and you can then restore after syncing the replacement handheld for the first time.