Hi David, thanks for your step-by-step solution BUT the notifications aren't being sent out (The Auto-response works perfectly fine)
I have done the following:
1. Updated Ticket.pm from v 1.412 to v 1.416
2. Selected the following on Admin=>Notification (Event):
    Recipient : Customer
    Event : TicketStateUpdate
    State : Closed successful / Closed unsucsessful
    Subject: Ticket Closed! [<OTRS_TICKET_TicketNumber>](<OTRS_CUSTOMER_SUBJECT[18]>)
    Text: Hi <OTRS_UserFirstname>,
            Your ticket has been resolved by the support team as follows:
            <OTRS_AGENT_BODY>
           <OTRS_CURRENT_UserFirstname> <OTRS_CURRENT_UserLastname>
           (IT Helpdesk)

Any idea on what I could be doing wrong?

Michael