Gmail's archive feature allows you to save emails in your account without cluttering your inbox. To migrate archived mail to a new account, use Mail Fetcher, a free Post Office Protocol service included with Gmail that periodically checks up to five POP-enabled accounts and gradually imports all existing and new mail. Mail Fetcher doesn't offer an option to import only archived mail, but because it generally imports the oldest mail first, you may be able to turn it off before transferring messages from your inbox.
Enable POP3 service in your old Gmail account. Click the gear-shaped icon, choose “Settings,” and then select the “Forwarding and POP/IMAP” tab. In the POP Download section, select “Enable POP for All Mail,” and then click “Save Changes.”
Log in to your new Gmail account, click the gear-shaped icon, and then select “Settings.” In the Accounts tab, click “Add a POP3 Mail Account You Own.” When the pop-up window opens, enter your old Gmail address in the text box, and then click “Next Step.”
Enter your old account's username and password in the text fields, click the “POP Server” menu, and then select “pop.gmail.com.” If you want to label imported emails, select “Label Incoming Messages,” and then choose a label from the drop-down menu. By default the label is your old account's username. To archive imported mail, select “Archive Incoming Messages.”
Click “Add Account” and, when prompted, choose whether or not to send mail from your new account using your old username. If you choose “Yes,” follow the on-screen instructions to enter your account information, and then check your old account for an email containing a verification link. Follow the link in the email to enable this feature.
Monitor the account migration by periodically checking your new Gmail account. Click “More,” and then select “All Mail” to view archived and sent messages. Google doesn't specify how often it imports batches of messages, but the process usually takes about an hour.
Turn off Mail Fetcher when you no longer want to import mail from the other account. Click the gear-shaped icon, select “Settings,” choose the “Accounts” tab, and then click “Delete” next to your old Gmail username.
To filter messages by label, click “More,” and then select the label name. Gmail displays all new, sent and archived messages containing the selected label.