I've just had a nightmare as a result of following this advice.
I wasn't aware that when I copied the emails from 'On My Mac' back to newly created IMAP account, that the emails were also going to be transferred to server of new Email hosting service which had a MB limit. So when it reached limit it gave me notice that inbox was full. Result: 865 emails copies out of 1400+ emails.
Additionally, I didn't want my emails to be stored on external server. When I realised I had 'uploaded' my old emails to new Email hosting, I tried to copy them back to folder on my Mac.
Result, emails lost on way over (on IMAP) server...as copies were somehow lost because I deleted folder thinking operation was done (it wasn't). So when I got notice that Inbox was full, I had already deleted the folder on my Mac.
When I tried to copy them back...on one inbox it lost all emails (as it hadn't properly ever copied them over before crash.
Plus, I never wanted emails to be 'stored' on external server.....
So beware people that migrate from POP to IMAP. Emails are not stored only on your computer once you download them.
On IMAP what is 'downloaded' on your computer still stays on server. If you delete it from server it's deleted from your inbox as well. You retain your own copy only if you save it to own folder from inbox. UGH