Did some testing on your system. If you select Share then both are selected when you come back in. If you do not select share then both are not selected when you come back in.
I think it is because you have been specific with your conditions, checkbox_false.UID = 51, but not your actions where you just spawn on checkbox_false. Rather include another condition to pick checkbox_false by UID, this will then only spawn or destroy on the picked checkbox.
Run it in debugger mode, I am guessing that they global variables are all operating fine, it has to do with putting the ticks in the right boxes at the startup.