I heard a person say that the person who neglects his Salah that is does not pray does not inherit anything because he is a Kaaffir, as the Prophet, sallallaahu alayhi wa sallam, said: "The difference between a believer and Kaaffir is Salah."
But I have heard that the majority of Scholars hold the view that they inherit even if they do not pray as they are sinners but could not be deprived of the right which Allaah has given them.
I have come across a verse in the Quran in which Allaah Says, "I will forgive all the sins of the slave of mine if he shuns to do shirk with me."
So if a person who does not do shirk with Allaah but because of laziness does not offer Salah but recognizes Salah as obligatory, will he inherit the property or not, as the general meaning of the Quranic Ayah goes with it. And as such in the present world only 5% of the Muslim population of the whole world offer Salah. And also Allaah has given a fixed share of each one in the Quran which cannot be changed by anyone.
Please clarify and give the reasons why he will inherit or do not inherit. Also please can you give which scholars do not permit and which scholars permit their inheritance?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

We have already issued many Fataawa regarding the ruling on a person who abandoned and neglected the prayer either by rejecting its obligation or out of laziness. You may refer to Fatwa 84235.

It is known that there are three things which prevent a person from inheriting others; they are slavery, killing [the inherited person], and the difference of religion. Details on these matters could be found in the books of Fiqh.

The ruling about inheriting a person who abandons the prayer out of laziness is based on the difference of opinion among the scholars about him being a Muslim or a non-Muslim. The majority of the scholars who are of the view that whoever abandons the prayer out of laziness is not a non-Muslim, are of the view that it is permissible for him to inherit because he is a Muslim unless there are other impediments that prevent him from inheritance, and they are slavery and killing. So a slave does not inherit and a killer does not inherit the person he killed. However, the scholars who are of the view that whoever abandons the prayer out of laziness is a non-Muslim, are of the view that it is not permissible to inherit a non-Muslim as there is an impediment of inheritance, which is the difference of religion. Moreover, there are some differences of opinion amongst them [scholars] with regard to defining the "difference of religion.”

To conclude, the issue of whether a person who abandons the prayer out of laziness inherits or not, and whether he may be inherited or not, is something on which there is a difference of opinion amongst the scholars as regards whether he is a Muslim or a non-Muslim.

It is only an Islamic court which may decide about such an issue as it is the body which is appointed and entrusted to rule regarding such matters. 

Allaah Knows best.