WARNING to anyone who is using this guide to replace the batteries in their Braun Synchro shaver. The video guide stops at a critical moment - the point when you would actually replace the batteries!
It turns out that the batteries are glued to the orange circuit board, pretty firmly too. I wasn't too worried about this, I just angled in a screwdriver, twisted (hard), and cracked the glue seal. What I didn't realize was that the metal leads that connect the ends of the battery to the board, are soldered to the battery - so torquing out the battery broke the metal connector off the board. It snapped right at the base too - would be very difficult to fix without some decent soldering skills, which I don't have.
So my advice is simple - make sure to separate the batteries from their connections on both sides, before trying to remove the batteries. The metal connectors are quite thin and weak, and quite strongly fused, so good luck :-)