Is it really just the rear lambda? I read somewhere that someone also had a problem with the cooling unit and a few other things.
Broadband lambda occurred to me, but I'm afraid of other problems
Front lambda, the main one. Two wires from ECU to probe, new connector.
Immo off or pair ecu/cluster.
Changes in software do reflect your current engine hardware. Like MAF sensor (in my case, my narrowband ecu uses a different sensor from wideband ecu). Replace the sensor or tune yours.
Code out VVT if do not have (MUST do! If not, O2 regulation will be kept off).
Make fueling ok (different injectors on each ecu).
Some ME7logger logs for some small sanity checks because of different turbos tunes (K03 vs K03S).