Magic Chef, (Armstrong) did this in mid 1980's. 8 seer
a/c units. Could add selenoid valve near evaporator coil,
paralell with low voltage to condenser. When condenser stopped at end of cooling cycle, selenoid closed, trapping liquid line full of liquid refrigerant. Also required adding start assist kit on compressor. Next time on call for cooling, the refrigerant was there @ evaporator coil, ready to begin cooling cycle. They claimed this would raise seer to "9"
Does the condensing unit possibly have a scroll compressor? First generation scrolls required a solenoid valve to stop reverse rotation of the scroll when the thermostat cycled off. If you ever replace a scroll that has a solenoid you'll need to remove it as the new compressors do not require a solenoid valve.