I keep needing to find the instructions for this so I’m putting them all together in one place. The steps are gathered from here and here and assume that PowerShell is installed.
$LiveCred = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection
Import-PSSession $Session– this shows a couple of scroll bars as the O365 commands are loaded in to the PS session.
New-Mailbox -Name "Shared mail box name" -Alias shared_mail_box -Shared
shared_mail_boxalias shown above is used as the name of the mail box, eg
Add-MailboxPermission "Shared mail box name" -User HelloWorldSG -AccessRights FullAccess
Add-RecipientPermission "Shared mail box name" -Trustee HelloWorldSG -AccessRights SendAs
As the instructions say:
Note It may take up to 60 minutes until users can access a new shared mailbox or until a new security group member can access a shared mailbox
I have seen it take a few days in some cases although that may be user error or bad caching. Once the permissions flow through the new mailbox can hopefully be added to Outlook.