icloud mail sync

Hello markjarmuz,

Thank you for using Apple Support Communities!

We understand from your post that your iCloud emails are not syncing across all your devices when you move emails or delete emails. Make sure that all of your Apple devices are logged into the same iCloud account, that all of them are connected to a known good Wi-Fi network and all of them are updated with their latest software version. If the issue persists, test each device individually and see if you make a change on one device if the change is reflected on any of the other devices. Make note of which devices sync the change and which ones don't. Let us know the results so we can further assist you.

Best Regards.

I mentioned this problem some 5 weeks ago. I have no idea when it first started. I simply thought that "I" was the problem. I did mention that it appeared that the problem solved itself. It actually didn't, and now it's even worse.

https://discussions.apple.com/thread/252671477

How to transfer mails from Mac to iPhone / iPad , even they are signed in with same Apple ID and password say example1@icloud.com 

In iPhone go to settings > in password and accounts > click on add account you can select the desired account it could be gmail , enter gmail address and password and sign in it will prompt to check calendar , mail , notes , slide the box of it the apps data will start syncing .

there is an option fetch new data - push > in iPhone

You can connect the iPhone and Mac using usb cable and sync them https://support.apple.com/guide/mac-help/wi-fi-syncing-mchlada1d602/10.15/mac/10.15

https://support.apple.com/en-in/guide/mac-help/mchlde9a31f1/10.15/mac/10.15

The mails from Mac / iPhone will sync and take time ( the fast way is sync complete data ) they will be mirrored , you delete a mail from Mac it deletes in iPhone , make sure all the mails should be read ( no blue dots on each mail message ) https://support.apple.com/en-in/guide/mail/mail0025/mac

See the articles to delete mails from Mac https://support.apple.com/en-in/guide/mail/mlhlp1001/mac

And from iPhone https://support.apple.com/en-us/HT208661