If you are however planning to transfer your existing Gmail messages to another email service that doesn’t support POP3 based importing, you can make use of a simple Google Script that will auto-forward all your old messages, one by one, to your new email address.
Transfer Gmail

How to Transfer Gmail Messages – Step by Step

Download this PDF file for Access all step


To configure the script, log on to your old Google account and then follow
these steps:
1. Click here to copy the Mail Forwarding sheet to your Google Drive
(associated with old Gmail Address).

2. You’ll see a new Gmail menu in the Google Sheet. Choose Gmail ->
Authorize to allow the script to access your Gmail account.

3. Once the script has been authorized, choose Gmail -> Transfer and type
your new email address where the old messages are to be auto forwarded.
The Google Script will now run in the background and will auto-forward
every single message from your old @gmail.com address to the new one.
The script will add the label “cloned” to all the threads that have been
successfully forwarded. This is required to keep track of messages that
have been processed.
The transfer process, depending upon the size of your mailbox, may take
a few days to complete because of Gmail’s daily sending limit. The
messages in the Trash, Spam and your Sent Items folders are ignored.
Also, the “Transfer My Gmail” script works on your entire Gmail mailbox. If
you would like to auto-forward a select group of messages, see the
previous tutorial on how to auto-forward Gmail messages in bulk.