Grants Full Access and Send On Behalf permissions to shared mailbox for a user or distribution group members (Exchange Online)

Grant-SharedMailboxPermissions.ps1

function Grant-SharedMailboxPermissions ($mailbox,$principles) {

    Get-Mailbox $mailbox | Set-mailbox -GrantSendOnBehalfTo $principles

    foreach ($principle in $principles) {
        switch ((Get-Recipient $principle).RecipientType.ToString()) {
            "UserMailbox" { 
                Add-MailboxPermission -Identity $mailbox -User $principle -AccessRights fullaccess -InheritanceType All
            }
            "MailUniversalDistributionGroup" { 
                # Get all the group members
                Get-DistributionGroupMember -Identity $principle | % {
                    Add-MailboxPermission -Identity $mailbox -User $_.primarysmtpaddress -AccessRights fullaccess -InheritanceType All
                }
            } 
        }
    }

}