1. Login to Gmail and click on the gear and select Mail Settings in the upper right corner.
2. Click on the Accounts and Import tab, then select Import mail and contacts.
3. Type the email address to the account you are adding and click Continue.
4. Type the password for the other account. Click Continue.
6. Select the items you wish to import. The Add label to all imported mail field can be used so you can distinguish items that were imported from regular Gmail items. Select Start import when you’re ready.
7. The import process will start. Once it’s finished, click OK. Note that it may take up to 2 days for items to appear.
If you ever wish to delete the account from Gmail, you can go back under the Accounts and Import tab and select the delete option next to the account.