Car jerks and cuts off when transmission is shifted into gear

Does it do the same thing in drive? If you start it in Neutral can you drop it in drive or does it stall there as well? If so, the converter is the most likely cause. When they lock up and you put it in gear and it puts pressure to it, it stalls the vehicle. Just like it you let the clutch out of a manual with no throttle input.

We need a scan tool to confirm this because we need to look at the torque converter slip and see what it is doing.

If you don't have a scan tool then unfortunately the only way to confirm this is to remove it and inspect/replace it. However, this is the most common cause of this issue.

More then likely it will not have codes. They did not start setting gear ratio error codes until later in the 2000's. That means the TCM/PCM is commanding a gear and it expects to see a specific output shaft speed and when it doesn't it sets a gear ratio error.

So you are correct, that you will need to do this while it is acting up. You will need a scan tool capable of watching the torque converter slip or input shaft speed. Basically if the transmission input shaft speed match engine RPM then the converter is locked up.

I am not aware of how to confirm this without that scan tool so that is why it leaves us with just replacing it and retesting. Clearly not a desirable thing but it may be the only option other then having a shop look at it when it is acting up.

However, the fact that it does it in all gears and it is not that way all the time tells me that it is most likely the converter. That is not uncommon. I have seen this happen in some Chrysler Minivans where it only stalls one time when getting off a highway exit and coming to a stop. They stall and start right back up and are fine until the converter is fully engaged again and comes to a stop.