The heater boxes are basically the same between YJ and CJ so the cabling should be correct, although if I remember correctly, it is possible to install the control cable backwards when you make this change.
The heater and A/C are completely separate. Although the A/C unit looks aftermarket, it is factory. early production and CJ were dealer installed and used the same lower unit.
Power should come into the A/C unit, when the blower is switched on, power is also routed to the thermostat control and then energizes the A/C clutch. It's a pretty simple standalone system. If it suddenly quit working, the fuses would be the first place I look as well.