$perm.user will get results like "contoso\username", which cannot be identity of Get-Mailbox.
Try the following commands please:
$perms = get-mailboxpermission -identity user | Where{$_.User -like "U*" -and $_.AccessRights -Like "FullAccess*"}
$perms | select @{Name="User";expression={(Get-Recipient $_.user.tostring()).displayname}} | foreach{
get-mailbox $_.User | Select Name, Alias
}
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