How to determine exact amount of oil in a refrigerant system?

When they did mine, having fitted a new condenser and compressor, the first operation was to use the machine to evacuate the system and it reported X grams of oil.

Then it was tested to see if it held the vacuum (well actually pressure below atmospheric...)

After that the machine filled it with the refrigerant and oil as needed.

Provided we're speaking of an OEM AC system, there are refrigerant and oil tables available online, which list the correct oil amount for every car. If 130 mL (oil is measured in volume, not weight) is what you have inside the compressor (drain it into a graduated container to be sure, anyways), and the table lists 130 mL of oil for your car's AC, you're perfectly fine. Otherwise, make sure you have the correct amount of oil inside the compressor (keep in mind that having 10mL in excess or being short of 10mL won't hurt anything). The same compressor can be fitted on multiple vehicles with different lenghts of piping and this means that the oil amount can vary between vehicles, especially whenever the vehicle comes with a "rear AC" option.

If you have an instruction sheet for the new compressor follow it, but keep in mind that generally speaking, before the engine can be allowed to turn the compressor's shaft, you have to rotate the compressor's shaft by hand (rotate the clutch hub if compressor has a clutch, or pulley if it's clutchless) about 10 times clockwise and 10 times counterclockwise so that it's correctly primed and no hydrolock happens; and switch the blower fan on at maximum speed before engaging the AC (or turning engine on if compressor is clutchless; in that case also turn AC on before switching engine on)/maximum cooling if car has automatic climate control; the same for any rear AC system; all of this ensuring that the engine stays in idle all the time. This has to be done for 5 minutes. This is because the evaporator/evaporators has/have to be loaded with heat so that the expansion valve/valves is/are fully open and that huge oil amount that has been put inside the compressor is able to freely circulate through the system, fill all the components and then return to the compressor with little or no damage experienced by it... this is called running-in of a new compressor...

Also, make sure the oil provided inside the compressor is actual refrigerant lubricant, and not assembly oil...