The wisdom behind naming the stone the Stone of Isma'il (peace be upon him)

Question:
The questioner, Abu 'Adil, says: Shaykh, regarding the naming of the Stone of Isma'il, is there a basis for this?

Answer:
The stone was named "al-Hajar" (the stone) and "al-Hatim" (the broken one) because it is enclosed by the Ka'bah. When Quraysh wanted to rebuild the Ka'bah, they only used lawful money, so they gathered lawful funds, but it was not enough to build it on the foundations of Ibrahim (peace be upon him). So they built it in this state and broke off a part of it, or they claimed it, so that it would be on the side of the Syrian and Iraqi corners. They surrounded it because it is part of the Ka'bah, so that the circumambulation would not enter it and the obligatory prayer would not be performed in it, because it is part of the Ka'bah. This is the reason for its being named "al-Hajar" or "al-Hatim." As for its attribution to Isma'il, I do not know what the basis for that is. Yes.