Does the hadith: "Whoever fasts Ramadan out of faith and hope for reward, his past sins will be forgiven," apply to one who does not pray?

Abandoning prayer out of denial of its obligation is major disbelief (kufr akbar) that expels one from the fold of Islam, by scholarly consensus. As for abandoning it out of laziness, it is one of the gravest major sins. A group of scholars has stated that it is major disbelief (kufr akbar), while the majority hold that it is a lesser form of disbelief (kufr duna kufr) that does not expel one from the fold of Islam. One who abandons prayer is not deserving of the reward for fasting, due to the hadith: "Whoever does not abandon false speech and acting upon it, Allah has no need for him to abandon his food and drink." Abandoning prayer is the greatest falsehood, and it contradicts the perfection of faith and seeking reward from Allah.