Ruling on giving zakaah to a daughter through breast-feeding

If the man has children who are poor, it is not permissible
for him to give the zakaah of his wealth to them, because it is obligatory
for him, according to sharee‘ah, to spend on them and make them
independent so that they do not have to ask others for what they need.
There are some exceptions to this ruling; for more information see the
answer to question no. 105789
and 130207. 

This applies to one’s own children and grandchildren. With
regard to children through breastfeeding, it is permissible to give them
zakaah, because one is not obliged to spend on them. 

Ibn Qudaamah (may Allah have mercy on him) said: The scholars
of the ummah are unanimously agreed that relatives through breastfeeding are
mahrams. With regard to the other rulings connected to kinship through
blood, such as spending on maintenance, manumission, rejecting testimony and
so on, they have nothing to do with the relationship through breastfeeding,
because blood ties are stronger than it, so an analogy cannot be drawn in
all rulings; rather the resemblance is only in the matters referred to by
the shar‘i text. End quote  from al-Mughni. 

He also said (8/169): All of the scholars from whom we
learned are unanimously agreed that a person is obliged to spend on those of
his children who have no wealth. With regard to spending being obligatory,
three conditions must apply… the third of which is that the one who spends
should be an heir. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

Breastfeeding does not make any of the rulings to do with
kinship applicable except those that have to do with marriage only;
breastfeeding creates the relationship of mahram, makes it permissible to
look (at the person) and haraam to marry that person. But it does not make
the people concerned heirs of one another or mean that one is obliged to
spend on the other or to pay the costs of diyah or to uphold the ties of
kinship, as in the case of blood relatives. Most of the rulings of blood
ties do not apply in the case of breastfeeding. End quote from Noor ‘ala
al-Darb. This has also been explained in detail in the answer to
question no 40005. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: 

Can zakaah be given to one’s mother through breastfeeding and
sister through breastfeeding? 

He replied: Yes, zakaah may be given to one’s mother through
breastfeeding and sister through breastfeeding, if they are entitled to
zakaah. That is because one is not obliged to spend on the mother through
breastfeeding and the sister through breastfeeding; so zakaah may be given
to them on condition that it be proven that they are entitled to it. End
quote from Majmoo‘ al-Fataawa, 18/417 

And Allah knows best.