From time to time you must fix a GUID or ImmutableID issue when migrating between AD domains, Tenants, and or federating services. When this happens and you end up with a soft delted mailbox for a specific user and you wish to restore it to their new mailbox you can initate a restore request in O365
$Alias = "<mailbox alias>"
$OldMailbox = Get-Mailbox -SoftDeletedMailbox -Identity $alias | Select-Object Name,Alias,ExchangeGuid,ExternalDirectoryObjectID,LagacyExchangeDN
$NewMailbox = Get-Mailbox -Identity $alias | Select Name,Alias,ExchangeGUID,ExtenralDirectoryObjectID,LegacyExchangeDN
New-MailboxRestoreRequest -SourceMailbox $OldMailbox.ExchangeGuid.toString() -TargetMailbox $NewMailbox.ExchangeGUID.toString() -AllowLegacyDNMismatch