A Linked mailbox is a mailbox that is associated with an external account. Thus Linked mailboxes are normal mailboxes that can hold an External account in a separate resource forest.
Few of these mailboxes here were shown as Linked mailboxes after migration because an orphan Active Directory Account has the "Associated External Account" right on the mailbox in question.
set-mailbox -id MAILBOX_NAME -ApplyMandatoryProperties
Now we come to why few mailboxes are shown up here as Shared mailboxes. If you have Self permission with associated external account checked, you get the shared mailbox on migration. That is the reason these mailboxes are showed up as shared.
Now we come to why few mailboxes are shown up here as Shared mailboxes. If you have Self permission with associated external account checked, you get the shared mailbox on migration. That is the reason these mailboxes are showed up as shared.
To fix this, remove the "Associated External Account" permission from the Self and again run that command:
set-mailbox -id MAILBOX_NAME -ApplyMandatoryProperties