Divios: Thanks, figured it out. The confusing part was that I did apply for beta, but never got an invite. I wouldn't expect the version number of the older client (non 2.0), to patch beyond what was publicly available. I guess both versions of the client are in beta.
There is the Galaxy 2 beta (what the invite was for) and the beta-branch of the current Galaxy (1). The latter can be enabled in the options which you seem to have done, but your friend hasn't. Just because Galaxy 2 is in development doesn't mean Galaxy 1 is "frozen". ;-)
So, either you install the normal stable release of Galaxy 1, or your friend also enables the beta channel for his Galaxy and updates to 1.2.62 BETA too.