The belief of a Mukallaf (legally competent person) that vowing or slaughtering sacrificial animals to those buried in graves is permissible, is considered Shirk (associating others with Allah in His Divinity or worship) which takes him out of the fold of Islam. He should be asked to repent for three days and to be kept under firm control. If he does not repent, he should be killed. With regard to the son's reception of the property of his father and inheriting from him after his death, this is based on the reality of the creed the father followed before his death. If the father dies while believing in this false creed, and no one knows for a fact that he had repented, the son is not allowed to inherit from him. This is because the Prophet (peace be upon him) said:
“A Muslim should not inherit a disbeliever, nor a disbeliever inherit a Muslim.”
(Related by Al-Bukhari and Muslim).
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.