Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello, I'm Diane, an M365 Apps & Services MVP specializing in Outlook.
Both VM and Outlook email accounts are IMAP and are set up in the Outlook mail client. <<
Is the Outlook.com account added as IMAP or exchange? Check in File > Account Settings > Account Settings > email tab.
If you are moving mail into the outlook.com account, you should use Exchange account type - IMAP doesn't always sync everything up.
As a backup, I would export the VM account to a pst file - file > Open & Export > Import and Export > Export to a file > choose PST. This will be insurance if you can't find a message in outlook.com. But before you do this, check in File > Account Settings > Account Settings. Double click on the account and make sure the sync slider is set to all. Otherwise, you will only export what is in outlook. (The same applies to moving mail to outlook on the web.)
Also, when you export IMAP accounts to pst files, the folders will appear empty - change the view on the folder to see the mail.