A typical alarm line will have be wired to an RJ31X 8 wire jack with a pair going to the jack and a pair coming back. For the alarm panel to be able to seize the line, normally the dial-tone from the phone block will be wired to the Red/Green pair first. Then the dial-tone will return on the Yellow/Black wires. The fax machine should be connected to the Yellow/Black wires. This would ensure that in case of an alarm the panel can disconnect the fax line and call out to the monitoring station.

There should be a surface jack outside the alarm panel. This is the RJ31X. If you disconnect the RJ45 cable then there are shorting jumpers that should connect the incoming Red/Green pair to the outgoing Yellow/Black pair. This way the dial-tone should still pass through if you unplug the alarm panel.

If you connect the Red/Green wires to the phone block but you don't get dial-tone on yellow/black, see if you can find the RJ31X jack and unplug the RJ45 plug. It should be outside the alarm box, but sometimes they put in in the box.