An 'experiment'-
Take the tube off going from the SC to intake manifold.
Take the TB off the SC and bolt it to stock location.


This essentially takes the SC out of the equation. See how it idles.

Today is my day off and i am planning on changing the IAT, fix and rearrange the vacuum lines take it for a drive and then i am going to do that you told me. But i think not sure though that its the IAT! There is no other sensor in my jeep i haven't changed.

Cross my fingers.....

Ok! I did everything! nothing changed! But i have a code 27#6 now. I can not short it out. Tomorrow i am going to the AEM installer. The code analysis is that

27 Injector circuit isn't switching when it's told to (TBI)
OR (MPI) injector circuit #1 not switching right
OR (turbo) injector circuit #2 not switching right
OR (all 1990-) injector output driver not responding
- check computer, connections

Well nothing still nothing happened.
I Will try the distributor now for cracks the ignition coil is new and heavy duty.

Did you try it with the SC 'out of line'.

Yes same thing happened! I am almost sure that it is an electrical problem.

FWIW, I am 99% sure it is a tuning issue.

Have you tried playing around with the fuel map at all?

Do you have the O2 sensor "clamped" correctly with the AEM?

What about an O2 sensor map? You will need one to dial in short and long term fuel trim corrections.

Edit... I just noticed you mentioned your AEM installer. If they have experience with the FIC, they should have no trouble locating the issue.

Could a faulty PCV cause that

Well the problem is not with the Map i am sure! It started having this problem a long time after we installed AEM.
I have two O2 one for Aem and wideband and one for the factory ECU. I am not sure if that is a problem? I might have burnt the factory O2! But i am unplugging the factory O2 when the problem starts and nothing happens.
I am trying to understand what the PCV would do to RPM's! Because i think that my PCV is stack closed! I will try to change that tomorrow. When the problem appears again.

I doubt the PCV would cause the issue, but I've seen weirder stuff happen for sure.

A dead O2 sensor can definitely cause the issue however. An exhaust leak up stream of the sensor can as well. Under normal conditions the ECU is using the sensor to adjust the fuel map.

should i use only one O2 sensor or it does not matter? The fuel is ok when the problem appears i push the throttle and it goes really rich!

well that's it i have changed everything all the sensors fixed the vacuum replaced almost everything except sparks spark plugs and distributor.
I am thinking of a intake manifold leak or crack or something like that. Would that create the problem?

Update
 

The problem is on the injector circuit. Now i have to find out about that.

Updates
 

I have finally found the problem! It was my distributer! The work shop did nothing so i have found out the problem my self. I have changed my distributer with the one from my spare parts xj and problem solved!

Congrats. Now enjoy your xj !