Bukhari

Hadith Commentary:
The meaning of the chapter is thus established: that an entire goat was sent to Nasibah as charity (sadaqah).
Now, when Umm Atiyyah sent a small portion of meat from that goat to Aisha (radi Allahu anha) as a gift,
it is derived from this that even a small amount of meat can be given as charity, because Umm Atiyyah’s sending it to Aisha (radi Allahu anha) was not charity but a gift.
Thus, charity is analogized upon this.
Ibn Munir said that Imam Bukhari, by bringing this chapter, refuted those who consider it disliked (makruh) in zakat to give so much to a single poor person that he becomes a possessor of the nisab (minimum amount liable for zakat).
This is narrated from Imam Abu Hanifah, but Imam Muhammad said there is no objection in this.
(Wahidi)
The Messenger of Allah (sallallahu alayhi wa sallam) declared the meat of that goat lawful to eat because when a poor person sends something as a gift from such wealth, it is permissible.
For, with the change of ownership, the ruling also changes.
This same subject is also mentioned in the hadith of Barirah (radi Allahu anha).
When Barirah (radi Allahu anha) sent meat given as charity to Aisha (radi Allahu anha) as a gift, the Prophet (sallallahu alayhi wa sallam) said:
هُوَلها صَدَقة وَلَنَا هَدیة
(Wahidi)

Hadith Commentary:
(1)
This heading has two components:
➊ The amount of the gift ➋ The giving of a goat.
The second component is established by the giving of a goat as a gift, and regarding the first component, there is no specification; whatever is available may be given to the needy. Therefore, no hadith has been presented regarding any specification of the amount.

(2)
It is also established from this that with the change of ownership, the ruling also changes, because charity and alms are forbidden for the Messenger of Allah (sallallahu alayhi wa sallam). However, when the needy person received charity and then gave something as a gift, by doing so, its ruling changed and it became permissible for the Messenger of Allah (sallallahu alayhi wa sallam) to use it, because such wealth is not subject to the rulings of zakat (obligatory alms).

This same subject is mentioned in the hadith of Barirah (radi Allahu anha), upon which Imam Bukhari (rahimahullah) will later establish a separate chapter: when the form of charity changes, what is its ruling? (Sahih al-Bukhari, Zakah, Chapter: 62)

It should be noted that Naseebah (radi Allahu anha) herself is Umm Atiyyah (radi Allahu anha), as Imam Bukhari (rahimahullah) has clarified in one of the manuscripts of this book.
(Fath al-Bari: 3/390)