Problem
You need to list all full, send as and send on behalf of mailbox permissions for a user in Office 365
Solution
$user = "username"
$Mailboxes = Get-Mailbox
#List mailboxes with full access
$Mailboxes | Get-MailboxPermission -User $user
#List mailboxes with Send As right
$Mailboxes | Get-RecipientPermission -Trustee $user
#List mailboxes with Send On Behalf Permission
$Mailboxes | ? {$_.GrantSendOnBehalfTo -match $user }