I jave an 88 240 sedan that just had another motor installed. It starts and runs well. When you either go to pull out or just increase the rpm's, it acts like it is shutting off for a second, then comes back and is completely fine until it is shut off again. Everytime it is shut off, you have this hesitation one time. No one I hae talked to has any clues. Help!!!

I have an 86 240 that does this, exactly the same problem you have. So far I have replaced the AMM, FPR, spark plugs, cleaned the throttle body, inspected for vacuum leaks, with no luck.

A few weeks ago my brick was getting terrible gas mileage and had problems idling, but I also noticed the weird stall didn't occur. After I replaced the FPR, the car ran great but the stall came back.

My 87 does something similar to this at times.... it's a little grumpy on that first start, then behaves fine the rest of the trip. I've almost stalled it getting out of the driveway. I'm about to embark on a quest to prevent all vacuum leaks and it may be a good idea for you as well.
Replace the intake manifold gasket ($3 at FCP Groton) and the injector seals (4X $2 each). Remove and inspect the intake air hose from the AMM to intake- if it's got pinholes or splits replace it ($14). Clean the throttle body and breather (flame trap) if you've not already done so. (I have, no effect on this behavior).
These are simple and cheap things you could do yourself, or wouldn't be real expensive at a shop. After that, I'd have to suggest making certain you have good fuel pressure and also replacing the fuel filter if it's old. (I haven't done those things yet, but should).
Good luck!
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Rob Bareiss, New London CT ::: '87 244DL/M47- 221K, 88 744GLE- 202K, 91 244 181K, 88 244GL 145K