Typically, incorrect permissions on the root Public Folder are the cause of "Access Denied" errors for an Exchange 2013/Microsoft 365 Destination.

Follow these instructions to set the correct permissions: 

1. ​​Log in to the Exchange Administrative Center.
2. Navigate to the Public Folders section (left menu).
3. Click on the '...' action (the '...' only shows up once a Public Folder mailbox has been created).
4. Select Root permissions.
5. Add the administrator as an owner to the root Public Folders, and checkmark the box for applying changes to all subfolders.​ Once this is done, you should no longer get the 'Access Denied' error when performing migrations.