Next to move mail on MAC from one email account to another

This is on MacBook Air with Sierra 10.12.6

The user filed saved mail "On My Mac" instead of in the Exchange Account.  There are several layers of folders.
Copying folders from "On My Mac" to the Exchange account is not reliable.  A lot of folders never get copied.

I know that I can re-create the folder structure in Exchange, and then manually move all the email one folder at a time, but that is a lot of work.

Is there a 3rd party program or some other method for moving all this mail?

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You either do it now and return the messages to the server, or do it every time the user gets a new laptop as well as be concerned on backing up the user's laptop data if you are in an industry subject to regulation...
Check whether the use's account setup type? an option could be to setup a new account using IMAP if the prior was not, and copy the directory structure from the email client to the IMAP account which will transfer the data back to the server.
Make sure you do this only after you disable the current account's settings from checking the server for new message.

once the process completes, the data will be back on the server.
imapsync could be an option, though the emails on the mac have to be stored in a particular way.

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If it's IMAP, then move all the mail to the server's IMAP folder, then move them back out again.  If it's POP, then you should get an IMAP account and move them to the IMAP account, then you can move them back.
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