Let me see if I understand this. The alarm circuit going to the M1 zone is in parallel with the resistor and relay - the resistor and relay are in series. The alarm circuit is usually open. The relay has power when the device has power so it is normally closed. That allows current to flow through he resistor and is picked up by the Elk as device ready. When the device trips, it shorts the alarm circuit so that more current flows through the short setting off the alarm. If power is lost to the device, the relay opens thus creating an open circuit that is picked up by the M1 as device trouble.
OK, now of the 11 terminals, which gets connected to which? 5 & 6 seem to be one side of the alarm circuit, while 7 & 8 are the other side of the alarm circuit. If the relay were not involved I could see putting the resistor between 6 & 7 and connecting the M1 zone wires to 5 & 8. That would put the resistor in parallel with the M1 zone wires.
Since the relay and the resistor need to be in series, I would think the resistor needs to go from 6 to 10 and then a wire from 11 (relay closed) back to 7 to complete the parallel resistor-relay circuit. Is it possible to damage the M1 if the detector wires are screwed up?