Is the fast of one who fasts Ramadan and prays in it valid, then abandons prayer as soon as it ends?

Prayer is a pillar of Islam. Whoever abandons it, denying its obligation, or out of negligence and laziness, has committed an act of disbelief (kufr). The fast of one who does not pray is not valid, except in Ramadan; rather, they are disbelievers because of that, for the Prophet, peace and blessings be upon him, said: "The covenant between us and them is prayer; whoever abandons it has committed an act of disbelief (kafar)." And he said: "The head of the matter is Islam, and its pillar is prayer." And he said: "Between a man and disbelief and polytheism is the abandonment of prayer."