Mirror Macbook Air to iMac screen

Hi

I want all of the email on my iMac to be accessible via my Macbook Air-is there an easy way to do this?

My iMac has been running extremely slowly and the folks at the genius bar want to wipe the hard grive and reinstall Catalina. I use it for business and want to save the emails, hoping that I can transfer them to the Macbook

Thanks