If your MKII was still working, I'd say to wait until the red LED light on the MKII goes out before unplugging it.
Otherwise, just unplug the old, plug in the new MKIII (with the antenna cable) & you're good to go.
No special coding needed, nothing to "synch up".
It may take a bit for your new MKIII to see the new sattelites in your area unless the MKIII came from very close to where you live.
2000 740iS. MKIV, 16x9, DDEs controlled by Euro fog light switch, reversed steptronic +/- pattern, paddle shifters, clear corners, Basslink, iPod video with stereo audio, TV tuner, gauge rings, ///M pedals, backup camera with 'on demand' switch, quad brake lights, Dinan engine & tranny software, windows/sunroof close via remote.
2003 540iS. MKIV, 16x9, PDC, CWP, TV tuner, backup camera with 'on demand' switch, paddle shifters, windows/sunroof close via remote, iPod video & audio.