Sounds like you're unfairly blaming the charging system. In your replies, please list exactly what's happening. "But it didn't work" and "with no result" don't tell me anything.
First, to test the charging system, use an inexpensive digital voltmeter to measure the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. That's just the first part of the test but it's enough to verify the battery won't run dead while you're driving. You need a professional load tester for the rest of the tests, but that isn't pertinent to this story. A good, fully-charged battery, with the engine off, will measure 12.6 volts. If it stays at that voltage when the engine is running, we'll have to diagnose the charging system. You have a GM generator that was redesigned for the '87 model year and is a disaster. We'll discuss that further if necessary.
Next, your vehicle is right in the middle of when Chrysler was buying AMC. AMC used parts from other manufacturers and put cars together with a mix of all kinds of stuff. Chrysler fuel pumps very rarely quit once they've started running, so you'll seldom solve a stalling problem by replacing it. When they fail, they fail to start up leaving you stranded in your driveway. Banging on the gas tank usually gets them going again. You could also have a GM fuel pump. They have a reputation for starting up but quitting while you're driving, leaving you stranded on the side of the road. If you have a GM pump, it could cause stalling. When that stalling occurs, turn the ignition switch off, don't turn it back on, then pop under the hood and check for fuel pressure. There's usually a test port on the fuel rail on the engine.
A better method is to borrow a fuel pressure gauge from an auto parts store that rents or borrows tools, and drive around with it clipped under a wiper arm so you can watch it. If the pressure suddenly drops, then the engine stalls, suspect the pump. I looked up a picture of your pump and it doesn't look anything like the Chrysler pumps I'm familiar with.
For the next part, you did yourself a disservice by removing the battery. That will have erased any stored diagnostic fault codes. At this point you'll have to drive the vehicle again and hope the codes set when the stalling occurs. I said "hope" because the most common causes of stalling often don't set codes, at least not the first time. It looks like you have a diagnostic system similar to Chrysler's. They make it easier than any other manufacturer to read the fault codes yourself. Go to this page for the instructions:
The only thing that looks different from Chrysler is having to wait five minutes to reread the codes. On Chryslers, if you think you miscounted the flashes, just turn the ignition switch off and back on once and it will start all over.
The most common causes of stalling while you're driving are the crankshaft position sensor and the camshaft position sensor. They often fail by becoming heat-sensitive, and will work again when they cool down in about an hour. The clue is there will be no spark. You didn't mention anything about checking for that.
You ARE going to have another problem with hard starting and stalling due to the idle speed being too low but we'll take care of that later. The fix is real easy, but in the meantime, you may need to hold the accelerator pedal down 1/4" to get the engine started and keep it running. (1/4" is plenty. More is not better). Disconnecting the battery caused this. While you are going to have this issue, it's not the cause of your stalling problem based on your comment, "but on the drive back, while I was giving it gas, the jeep died on me again". Giving it gas is the clue. This new problem I'm talking about is due to idle speed being too low. The engine will run fine when you're pressing the accelerator pedal.
Monday, October 13th, 2014 AT 8:02 PM