Do enlightened beings have no desires? Are all of their desires already fulfilled?

The ultimate desire every soul yearns for - unknowingly or knowingly is to be free - Free from cravings and aversions, likes and dislikes. An enlightened being is free from all such dualities as he has realized that source of happiness is within- he is happiness himself. He has realized the kingdom of heaven within. Nothing external , no desire can create any more happiness than that is already present within. For an enlightened being, desires are fulfilled even before they arise. Just like many rivers flow into ocean, but the ocean remains unperturbed, all the desires flow into such beings but they remain least affected/perturbed.