Follow the instructions in the video to move your email from one Google Account to another. Note that the process takes a little while depending on how much e-mail you have in the initial account. This process will continue to work until your initial account is closed/deleted. If you prefer written instructions, check this page by Google Support.
Note that you can decide if to keep messages in the original e-mail account, and how to organize transferred mail (into a folder and/or into archives).
Thanks to @blacklinemaster for the video recommendation.