What lessons can other countries making the transition from authoritarian rule to democracy learn from Germany?

Probably none. It's certainly not a blueprint for other countries. The situation in Germany was most unusual in two respects: 1. Germany had an earlier (though unsuccessful) democratic tradition of sorts. 2. The country that had prided itself on its cultural, academic and scientific achievements, the country that had liked to see itself as the pinnacle of civilization, was exposed as morally bankrupt through and through.