Your Mail account information (and pretty much everything else related to accounts) are stored in Keychain. At the moment I don't have time to provide very specific step-by-step instructions, but if you want to import that information go to ~/Library/Keychains/ and import that entire folder's contents from the account containing your Mail account information. Before you do that be sure to archive that existing folder – do not overwrite it. Expect some consequences from that action, such as having to enter login information for all other services that require authentication. It would be a good idea to back up your Mac before doing anything.
Another, probably more reliable way of accomplishing what you want would be to use Migration Assistant to migrate account information to a brand new User Account. That Account would need to have a separate name from the one you are now using. Then, you could log into that Account, delete what you did not want to migrate, make sure that everything works the way you expect, and only then delete your other Account. Then, you could change the "short user name" of that User Account to one you wish to use.
The following Apple Support documents explain those procedures:
OS X: Manually migrating data from another Mac - Apple Support
Move your content to a new Mac - Apple Support
macOS Sierra: Set up users, guests, and groups on your Mac
macOS Sierra: Delete a user or group
Change the name of your macOS user account and home folder - Apple Support
It bears repeating – back up your Mac before doing any of this.
