Oh, I’ve been stupid. The problem is solved. I saw in one of the tutorial videos that you can unscrew the Smart logo side of the key fob with a slight twist between the flat of the hands. But I couldn’t get it to work. Finally, I looked at it closely and found that the guy was unscrewing with a CLOCKWISE turn! What? Whoever heard of unscrewing clockwise? Well, it works really easily.
So I’ve replaced the battery. All ok.
BTW, I see that the fob also contains a small mechanical key that will open the car door in an emergency.
