I just got this great question from one of my teachers:
Is there an easy way in Gmail to forward a folder full of emails to another email address?
There is a way to save and move those messages, but not how you are describing… Google has a service called Google Takeout (https://takeout.google.com/
Getting those emails back into another Gmail account is more of a process. There is no way to import directly an email archive (you would think that would be the case since you can create and download said archives…). This is the best article that I found explaining the steps to import them into a new account using the free Thunderbird email program.
And… Now that I’ve written and researched all of this, I did a bit more research and found an easier solution. There is a Chrome browser extension called Multi Forward for Gmail that will allow you to select multiple emails to forward at once. Read the reviews for some tips on how to use and it’s limitations (you can only forward 100 messages/day). Let me know if you try it and it works for you!