Black smoke is VERY rich. When my 745 acts up it gets about 15mpg, but runs fine and no visible smoke. Not sure how the mechanic evaluated the AMM, but using a VOM on the O2 sensor should confirm whether it is working. I think there is a voltage to be read off the AMM also, but not sure where that info is.
As Robert said the rebuilt AMM's have a bad rep, I got a used Bosch one for $65 which has been fine. It probably is not the AMM, since both being bad the same way is unlikely. Does the rich running come and go? Maybe there is a bad connection to the ETC or the O2 sensor. I'd check these with a VOM at the ECU when the problem occurs. (turn off the power when disconnecting the ECU).
The only other item I can think of is a fuel injector which is sticking open intermittently.
Another thought. Is the ignition system firing correctly? Is that black smoke from unburnt fuel.? Does the car have normal power and run smooth?
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744 & 745 16v 4+OD, 245 SE auto, 242Ti 4+OD, 745 8v auto (new), 245DL auto parts car