I want to update Facebook through my twitter - that is, whenever I post something on twitter, I want it on my FB wall.
However, the "default", official way does not work for me due to error described here http://stackoverflow.com/questions/15361703/twitter-to-facebook
What you are describing is a known bug Twitter bug.
The problem comes up when your Twitter account was previously connected to another Facebook account that you deleted/deactivated without removing the Twitter app first.
which is true for my case.
The error I get is
Facebook reported an error. The error has been reported to our engineering team. Please try again as it might be a temporary problem.
However, if I search for some other app offering synchronization on Google, all I find are tutorials for this official way. So, my question is - is there another way that works too?