No, that's not it. It's called the EWS "transmitter" part#61358379502 or 61358362337(ended) and it's located near the steering column. Item# 3 in this diagram:
http://www.realoem.com/bmw/showparts...33&hg=61&fg=25 Marv17 had the same problem. He swapped his ews transmitter with the one from his donor car by mistake and his car wouldn't start. Then he noticed that when he layed the donor car's steering column on the floorboard in his ti, the ti would start. It's because the donor car's steering column still had the matching antenna ring installed, lol. I told him to either swap the antenna ring or put his old transmitter back in. His car started right up with no problems.
The transmitter and antenna ring typically don't need to be swapped. That's where the confusion happens. The only things that need to be swapped during an engine swap process are the ecu, key transponder chip and ews control module behind the glovebox. When people swap the antenna ring as in your case due to the spinning ignition barrel, they also need to swap the ews TRANSMITTER or reuse their old antenna ring.