All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The person who does not fast in Ramadan commits a great major sin no matter how punctual he is with the prayers. In fact, fasting is one of the five pillars of Islam, and all Muslims should observe it and should give it a great importance. Anybody who does not fast in Ramadan should make up for what he has missed. He should also abundantly seek the forgiveness of Allah.
As for the prayer of a person who does not fast, it is valid according to the scholars who are not of the view that giving up fasting is synonymous to disbelief. The opinion of these scholars is the preponderant one as there is no evidence which proves that abandoning fasting reaches the level of becoming a disbeliever. But, as we said, it is a great major sin and you should repent from it immediately and make up for all the days you have missed.
For more benefit, please refer to Fataawa 82013 and 82187.
Allah knows best.