The opinions on whether the post cat O2 sensors have anything to do with fuel trim is another one of those long debated issues.

The Bentley service manual for 2000 to 2006 X5s states that O2 sensors contribute to fuel trim. It does not designate between pre and post. It is a general statement. It is generally accepted the post cat sensors monitor emissions. Seems if the intention is too monitor emissions and conveys that reading to the ECM it is not just for grins.

That said, with OPs symptoms, it could be the post O2 sensor but there is a possibility if could be the cat. I suggest disconnecting the post O2 sensor and see what happens.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas