Can he give his zakaah to his brother on whom his father spends?

Giving zakaah to one’s deserving relatives is better than
giving it to those who are not your relatives, because charity given to a
relative is both charity and upholding the ties of kinship. But if these
relatives are among those on whom you are obliged to spend, then it is not
permissible for you to give your zakaah to them. 

See the answer to question no.
20278 

Spending on your brother is obligatory for your father, but
if your father is not able to spend on him, it is permissible for you to
give your zakaah to him.  

The scholars of the Standing Committee were asked: 

My father died (may Allaah have mercy on him), and left
behind a family of seven people, including another wife besides my mother.
They do not have any source of support apart from Allaah. Is it permissible
to regard what I spend on them of my own money as zakaah, knowing that I am
married and support another family of my own? 

Secondly: I have an older brother who is married and has two
wives, and he has a lot of children and can hardly afford to look after
them. He often asks me for help. Is it permissible to regard what I send to
him as zakaah? 

They replied: 

There is no reason why you should not send zakaah to your
siblings through your father, both males and females, in the future, if they
are poor and do not have sufficient wealth to render them in no need of
zakaah. Similarly it is permissible for you to send zakaah in the future to
your older brother if he is poor and has no wealth or earnings to render him
in no need of zakaah, because of the general meaning of the verse on zakaah,
in which Allaah says (interpretation of the meaning): 

“As-Sadaqaat (here it
means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor)
and those employed to collect (the funds); and to attract the hearts of
those who have been inclined (towards Islam); and to free the captives; and
for those in debt; and for Allaah’s Cause (i.e. for Mujaahidoon — those
fighting in a holy battle), and for the wayfarer (a traveller who is cut off
from everything); a duty imposed by Allaah. And Allaah is All-Knower,
All-Wise”

[al-Tawbah 9:60]

Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd al-Razzaaq
‘Afeefi, Shaykh ‘Abd-Allaah ibn Ghadyaan. 

Fataawa al-Lajnah al-Daa’imah,
10/57, 58. 

Elsewhere they said: 

It is permissible for
you to give to your half siblings and wife’s father zakaah that will suffice
them, if their income is not sufficient for them. 

Fataawa al-Lajnah al-Daa’imah,
10/59 

Shaykh Muhamamd al-Saalih al-‘Uthaymeen (may Allaah have
mercy on him) said: 

With regard to your
question as to whether it is permissible to give zakaah to a half-brother or
full sister, the answer is that if giving zakaah to them  involves waiving
something that is a duty for you, such as if it is obligatory for you to
spend on them, and you give them zakaah so that you will not have to spend
on them and can save money, that is not permissible, because zakaah cannot
be a means to avoid spending. But if it does not, such as if you are not
obliged to spend on a person, because you are not one of his heirs, or
because you cannot afford to spend on him as well as your own family, or you
give it to him to pay off a debt that he owes and cannot repay, then it is
permissible for you to give your zakaah to him, and indeed that is better
than giving it to someone else, because giving it is both charity and
upholding the ties of kinship. 

Majmoo’ Fataawa Ibn ‘Uthaymeen,
18/422, 423. 

See also the answers to questions no.
21810 and
11492 

And Allaah knows best.