Trouble moving iCloud emails to On My Mac on iMac

I periodically move all gmail and iCloud mail from their cloud storage to Mail.app's Local mail at ~/Library/Mail. I do that by selecting desired messages in Mail.app and > Message > Move to (or Copy to) > some previously created Local mailbox.

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I also sometimes make a backup of Mail: zip (right-click > Compress...) the ~/Library/Mail folder or move that Mail.zip to another account.

Then in another account (if that account has no mail I often first delete the existing ~/Library/Mail folder there) uncompress that .zip by double-clicking it and:

Mail.app > File > Import Mailboxes... > Apple Mail > choose that uncompressed Mail folder > choose all Items.

On the left-hand-side under "On My Mac" > Import, ..., look for and move "Local" and all mailboxes inside it up under "On My Mac". Right-click and you might delete "Import" folder (it has gmail mailboxes that are online). YMMV.

Strgzr wrote:

If that is so, then why does the lists of emails listed below that "iCloud(IMAP)" (as pic shows above, like names "9-fluMaps 2024-2025, etc) are some very old ones not even currently in the folders I copied over to "On My Mac" in Mac Mail?

When you click the Account Info, even for a folder "On My Mac", you get the information for the account itself (iCloud in your case), not the information about the folder "On My Mac".

Click the Account Info by selecting your regular iCloud Inbox. You will see exactly the same list of folders in the Account Info window.

Strgzr wrote:

~(I guess that is my named home folder?)...so then ~/Library/Mail/MAILBOXES area the folders inside that (before I even tried to "compress") are not the names of folders currently in my Mac Mail App. They are some titles I think I had many years ago, as I remember such names but cannot find in my Mail App today. In fact I can't find any of my current mail folders in that Library LOC. I tried searching for an email inside one of folders showing in Mail App/On My Mac, and can't find that either. Why and Where to find current ones?

Local (and I guess also cloud mail) is stored there but the file and folder names are not human readable, they are for the computer to read.

As a test, make a dummy new user and let Mail.app import that whole ~/Library/Mail folder (instructions in my previous post).

I use that method to move local mail to a new cleanly installed computer although Migration Assistant should do the same.

Even though, the Account Info in a folder in "On My Mac" will display the source of the folder, e.g. "iCloud (IMAP)" in your example, the folder is independent from the iCloud email server. Emails moved in that folder reside only on your Mac and are no longer on the iCloud email server (so they no longer take any storage space on iCloud.)