Battery warning light is on and it stalls

So if I understand correctly, the battery warning light turns on intermittently, and the alternator has already been replaced. If that's right, you have to do any testing while the problem is occurring, (the light is on). The entire system can be diagnosed by measuring the voltages on the two small wires on the back of the alternator. You'll need an inexpensive digital voltmeter. Measure the voltages on each wire. Those MUST be taken while the engine is running. One will have full battery voltage on it, around 12.6 volts. The other one must have less but not 0 volts. 4 - 11 volts is typical. If you find 0 volts or exactly the same voltage as on the first wire, we can figure out where to test next.