I promised an update on my earlier problems with the new battery charger. It appears that .............
1. The BMW Dealers' battery chargers are different from the ones we can buy. Theirs will charge any BMW battery, but cost around twice as much as the ones we get.
2. My problem, which was similar to Happy Grandad's, was that the charger stayed in de-sulphinating mode for 12+ hours. And then seemed to go straight to the maintenance mode (HGrandad's charger ended up showing the error light whereas my didn't). Even having been fully charged, the battery still seemed to get locked into the desulphinating mode. After research & discussions with BMW, it appeared that either "1) the charger is knacked, or 2) the battery is knacked, or 3) the bike (electronics) is knacked" (see earlier posts).
3. My dealer reloaded the bike software, which took some time. Incidentally, this has completely cured the '2500rpm lurch' which has been mentioned on a different thread. The dealer then replaced the battery, and charged it using my charger - which worked perfectly. I have subsequently stuck the bike on charge through the aux socket and (so far) the system seems to work perfectly, the green 3/3 maintenance mode coming up in around 45 minutes. It seems, therefore, that the problem lay with my original battery. However, the software reload updated the bike charging map, so it is possible that the battery problem may have been caused by the original charging map in the bike; there's no way of telling.
Happy Grandad - get your dealer to reload your bike software completely, and get them to replace your battery with a new one.
4. The service engineer tells me that, if you disconnect the battery (say, to recharge using an Optimate) then, once reconnected, open and close the throttle fully twice (ignition on, engine off, obviously). This helps the management system 'recalibrate itself', or something like that.