Maintaining ties with a brother who does not perform the prayer

Q: My eldest brother does not perform the prayer. Should I maintain ties with him or not? Please note that he is my brother only through our father.

A: One who deliberately abandons the prayer is a disbeliever by major shirk (associating partners with Allah) according to the most correct of the scholars' opinions, provided he acknowledges its obligation. If he denies its obligation, he is a disbeliever according to all scholars; because of the saying of the Prophet (peace and blessings be upon him): narrated by Imam Ahmad and al-Tirmidhi with a sound chain, and because of his saying (peace and blessings be upon him): narrated by Muslim in his Sahih, and because of his saying (peace and blessings be upon him): narrated by Imam Ahmad and the people of the Sunan with a sound chain, and because the one who denies its obligation is lying to Allah and His Messenger and to the consensus of the scholars of knowledge and faith, so his disbelief is greater and more severe than the disbelief of the one who abandons it out of negligence.
In both cases, it is obligatory for the Muslim rulers to demand repentance from the one who abandons the prayer; if he repents, well and good, otherwise he is to be killed; based on the evidence regarding this matter.
It is obligatory to boycott the one who abandons the prayer, cut off ties with him, and not respond to his invitation until he repents to Allah from that, along with the obligation to advise him, call him to the truth, and warn him of the punishments that follow abandoning the prayer in this world and the Hereafter; perhaps he will repent and Allah will accept his repentance.