First, visit Gmail Help to set up Outlook Express client to work with Gmail (IMAP access) >> http://mail.google.com/support/bin/answer.py?answer=77659&topic=12761.
Follow the process to set up your main Gmail account and do it a second time to set up your secondary account. You will use it to back up your archive mails.
Step2
When you are set, click Send and Receive to fetch your mails from your main account to Outlook.
Step3
If you want to keep the same labels, go to your secondary Gmail account and create identical labels (Settings > Labels > Create a new label). Those labels should appear instantly in Outlook Express (Thanks to Google for their free IMAP service).
Step4
Select one of the label in your main Gmail Account (as shown on photo)
Step5
Hold Ctrl + A to select all your mails on right panel (or just select the mails you want to export).
Step6
Right-click on your mouse and select Copy to folder. Choose a folder on your secondary Gmail account to copy your messages and click OK when you are done.
Step7
It might take a while before the mails are exported to your secondary account.
Step8
Repeat steps 4 to 7 until all your archive mesages are saved on your secondary Gmail account. Be patient, it can take a long time to back up your full account to another one especially if you have thousands of mails as I do (I am still drinking coffee).
Step9
You can visit my website to see how to export your mails via Thunderbird 2.0: http://web-kreation.com/blog/?p=48
Tips & Warnings
It will take time before your Gmail messages appears in your email client