Leave a copy of retrieved messages on the server
While you’re setting up Gmail to check emails from other accounts, you can decide what happens to the emails in your other account after they’re brought into Gmail.
Importing emails from another Gmail address
If your other account is also a Gmail account, keep Leave a copy of retrieved messages on the server unchecked.
To control what happens to your emails, change your settings in your other Gmail account (the one you’re importing mail from). See directions for how to change your settings.
Importing emails from another email provider
Keep emails in your other account (recommended)
Check the box next to Leave a copy of retrieved messages on the server if you want to see your emails in both your other account and in Gmail. If this option is unchecked, emails in the other account will be deleted after they’re brought into Gmail.
Note: Some email providers may still delete your emails after they’re brought into Gmail even if this option is checked. Gmail will instruct the other provider not to delete the messages, but it’s ultimately up to the other email provider.