Thanks joemike….the old account was POP, the new one is IMAP
After posting I did a bit of poking around in Mail and, under "File" I found "Import Mailboxes". That opened a dialogue box with a number of mail choices (Apple Mail, Netscape, Eudora, et cetera), so I picked Apple Mail.
Then it was a matter of navigating through Users to the Library and the Mail Accounts. The import process took quite a while (15 years of mail) but it imported all the mailboxes complete with all the right folders. Neat.
The only puzzler was that I had an extra folder duplicating all the same stuff that I had imported. I just deleted that folder and all is well.
All in all, a good day.
EDIT: It looks like I'll be using your suggestion for my wife's email. She has a separate account on our computer and, when I went there, I couldn't see the User Library.
Last edited by ryck; 04/14/17 02:37 PM.