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Welcome to the Apple Support Communities!
If you are asking about emails ending with @iCloud.com, these are not included in an iCloud backup.What does iCloud back up?
Your iPhone, iPad, and iPod touch backup only include information and settings stored on your device. It doesn’t include the information already stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, shared photos, iCloud Photo Library, My Photo Stream, and files you store in iCloud Drive.
How to use the Mail app on your Mac to move, delete, or copy iCloud email
Copy email from iCloud to your Mac
- In Mail, choose Mailbox > New Mailbox.
- A New Mailbox dialog opens. Choose On My Mac from the Location pop-up menu, then enter a name for the new mailbox. Click OK.
- Select your iCloud inbox from the list of mailboxes in the sidebar, then select the messages.
- To copy messages, hold down the Option key while dragging the messages you selected to your new mailbox. Or choose Message > Copy to > your new mailbox.
If you want to make a backup copy your entire iCloud mailbox, including every message and folder in the mailbox:
- Select your iCloud inbox from the list of mailboxes in the sidebar.
- Choose Mailbox > Export Mailbox.
- Choose a destination folder for the mbox archive, then click Choose to save it.
Take care.
May 5, 2017 11:13 AM
Mail User Guide
Mail can import email messages that have been exported in mbox format from other email apps, and import mailboxes exported from Mail on a Mac. You can export mailboxes in mbox format.
Import mailboxes
In the Mail app on your Mac, choose File > Import Mailboxes.
Select a source in the list, read the information that appears below the list, then click Continue.
If you’re importing a mailbox exported from Mail or a folder in the ~/Library/Mail/V7 folder on another Mac, select Apple Mail. To get to the Mail folder on a Mac, click the desktop to make sure you’re in the Finder, press and hold the Option key, choose Go > Library, then click the Mail folder.
If you’re importing messages from a Windows or UNIX computer, select “Files in mbox format,” then locate the folder containing the files.
Reorganize the imported messages, if you like.
The messages are in a new mailbox called Import in the Mail sidebar. You can drag folders and messages from the Import mailbox to new or existing mailboxes, then delete the Import mailbox.
Export mailboxes
In the Mail app on your Mac, select one or more mailboxes, then choose Mailbox > Export Mailbox.
Choose a folder or create a new folder, then click Choose.
Mail exports the mailboxes as .mbox packages. If you previously exported a mailbox, Mail doesn’t overwrite the existing .mbox file; it creates a new .mbox file, such as My Mailbox 3.mbox.
Mail Backup Software For Mac