Do you care about the fan only setting to work and to you have A/C? If you don't use it, or don't have A/c it is much simpler to wire.
If you do use the fan only setting and want to use it in the winter, you will not be able to let the water always circulate through the heat exchanger.
To wire up with the fan option disabled, run a jumper wire from the original thermostat RH terminal to the RH in the 2nd thermostat. If both thermostats have C used then run a jumper between those terminals on both thermostats.
Then remove the wire from the G terminal and add a piece of wire to it and run that to the W in the new thermostat.
If you do want to use the fan only setting but only in the summer, you can leave the wire on the G terminal and run a jumper wire from it to the W on the 2nd thermostat. You will probably have to shut off the breaker to the A/C in the winter to keep it from running.
If you want to keep the fan only option and not have to turn off the a/c you will need to wire in a relay.