Without knowing the model of your F/F, I'd suggest that the original thermostat contol unit has three wires running to it, (ignoring the temp probe) Find the LIVE in, LIVE out and Signal wire that leads to the temp selector dial/power switch.
Remove these three wires and use the LIVE IN connector to provide permanent live to your new controller, Connect the Live Out connecter to the Live Out(compressor power) that comes out of your new controller. The third sensor wire may not be required and can be insulated and ignored if not.
The new controller's Neutral and Earth wires will need to be connected to the nearest available location on the mains power cable.
Rupert
November 2019