I've got the exact same problem.
Tried it every now and then for the last 30 hours or so!
fyi:The account I moved from MM to iCloud is one of my family member accounts.
hbu?
In order to get your mail online in iCloud working you first have to go to the preference pane on your mac for MM and logout of MM.
Then login to iCloud in the pane for iCloud.
then delete your MM account from the mail pane and add iCloud.