How do you if alternator is not charging?
Use a DVOM (Digital Volt Ohm Meter) to see how many volts are
output at the battery if it 13.3 to 14.4 the alternator is putting
out the right voltage.
Now you need to test that it is putting out enough amps, some
dvom s have an inductive pick up clamp you can use to read the
amps. Otherwise O'reilys, advance, pep boys auto parts will usually
test it for free while it is in the car