You can use the DC output of the RFX9600 and switch it through a relay on the RFX9600 to (with a jack cable) the APC S-15 to use it as a trigger. The APC needs dc current, not just a shortened circuit.

So 5v from RFX9600 dc output on the jack. GND from RFX9600 dc output to on side of the RFX9600 relay and the other side of the relay to the other cable to the jack.

Then if the the relay is closed the APC see's current and if it's open it has no current on the trigger.