Who was the philosopher that emphasised the importance of good moral behavior to build a well functioning society with each individual having the responsibility to do the right thing?

The correct answer is Plato

Plato is responsible for having access to the thoughts of several ancient Greek philosophers, such as Socrates, his master, Heraclitus, Parmenides and Pythagoras. Plato was also the introducer of the method of dialogue in philosophy and with his work The Republic founded Western political philosophy.

Plato was one of the most aware philosophers of how philosophy should be conceived and what its scope should be, and what ambitions the philosopher might aspire to. In fact, Plato can be considered the inventor of the theme of philosophy, what it actually deals with, having philosophy as a rigorous and systematic examination of ethical, political, metaphysical and epistemological issues through a distinctive method.