Is the 'Drafts' folder migrated, and how are draft messages displayed at the Destination?
The 'Drafts' folder is migrated as part of a mailbox migration.
It will be migrated over to a corresponding folder named 'Drafts' at the Destination, unless there is a folder mapping explicitly added which alters this behavior. Refer to KB005017 for more information on folder mappings.
The display behavior of draft items will vary depending upon the Destination.