Can a person who is Muslim in name only be given any part of the inheritance?

No part of the religion of Allaah may be forsaken because of differences in
time, place or circumstances, whether it be the laws of inheritance or
anything else. These rulings apply in all times and in every place, for
Arabs and non-Arabs, male and female, rich and poor, nomads or
city-dwellers; all of them are equal in this regard. When Allaah mentioned
the laws of inheritance in Soorat al-Nisaa’, He said at the end of the
aayah (interpretation of the meaning):

“(these
fixed shares) are ordained by Allaah. And Allaah is Ever All Knower, All
Wise” [al-Nisaa’ 4:11]

 Imaam Ibn
Katheer said in his commentary on this aayah: this is an obligation which
Allaah has enjoined and decreed. Allaah is All-Knowing and All-Wise, Who
puts things in their places and gives each person what he deserves
according to his own situation. “And
Allaah is Ever All‑Knower, All‑Wise” [al-Nisaa’ 4:11].
(al-Tafseer, 1/500).

 Then
Allaah says, concerning the rulings and amounts of inheritance
(interpretation of the meaning):

“These
are the limits (set by) Allaah (or ordainments as regards laws of
inheritance), and whosoever obeys Allaah and His Messenger (Muhammad) will
be admitted to Gardens under which rivers flow (in Paradise), to abide
therein, and that will be the great success.And whosoever disobeys Allaah and His Messenger (Muhammad), and
transgresses His limits, He will cast him into the Fire, to abide therein;
and he shall have a disgraceful torment} [al-Nisaa’ 4:13-14]

In
this aayah, Allaah states that not implementing the shar’i rules on
inheritance is a transgression of the limits set by Allaah, and that the
person who does this will abide in Hell forever and will suffer a
disgraceful torment.

You
must realize – may Allaah bless you – that knowledge of the
inheritance laws is half of knowledge, as some of the scholars said. Ibn
Katheer said: Ibn ‘Uyaynah said: the inheritance laws have been called
half of knowledge because all people go through this. (al-Tafseer,
2/497).

Secondly:

If you
believe that the person who does not pray is a kaafir and apostate –
which is the correct view, and Allaah knows best – it is not permissible
for a kaafir to inherit anything from a Muslim’s wealth, or for a Muslim
to inherit anything from a kaafir’s wealth.

It
was reported from Usaamah ibn Zayd (may Allaah be pleased with him) that
the Prophet
(peace and blessings of Allaah be upon him) said: “A
Muslim does not inherit from a kaafir and a kaafir does not inherit from a
Muslim.” (Narrated by al-Bukhaari, 6383; Muslim, 1614).

Based
on the above, those who do not pray cannot inherit anything from those who
pray regularly, and those who pray regularly cannot inherit anything from
those who do not pray.

Thirdly:

You should
find out whether this person who does not pray has forsaken prayer
altogether, or if he prays some of the obligatory prayers and neglects
others. If the latter is the case, then he is not a kaafir, because the
kaafir is the person who does not pray at all.

Fourthly:

From
the above it will be clear that upholding the limits set by Allaah with
regard to inheritance is obligatory in all cases, whether all the family
members accept this ruling or only some of them do so, because the ruling
of Allaah is fixed and definite. At the same time we should note that
everyone who does not accept the ruling of Allaah is a kaafir who cannot
inherit from his Muslim relative and his Muslim relative cannot inherit
from him, if he dies when he still rejects the ruling of Allaah and is still a kaafir. And Allaah knows best.