Question: Did Brigham promise that Joseph Smith III would eventually take over the Church?

Brigham was referring to being "ready to receive" any of Joseph's children into the Church

The Wikipedia article "Joseph Smith, Jr." makes this rather interesting assertion:

Indeed, as late as 1860, Brigham Young assured the bulk of Smith's followers that young Joseph would eventually take his father's place. (Journal of Discourses, 8:69.)

The source provided does not support the assertion that Brigham stated that "young Joseph would eventually take his father's place." Brigham said,

What of Joseph Smith's family? What of his boys? I have prayed from the beginning for sister Emma and for the whole family. There is not a man in this Church that has entertained better feelings towards them. Joseph said to me, "God will take care of my children when I am taken." They are in the hands of God, and when they make their appearance before this people, full of his power, there are none but what will say—"Amen! we are ready to receive you."
The brethren testify that brother Brigham is brother Joseph's legal successor. You never heard me say so. I say that I am a good hand to keep the dogs and wolves out of the flock. I do not care a groat who rises up. I do not think anything about being Joseph's successor. (Brigham Young, Journal of Discourses 8:69.)

Brigham's comment "we are ready to receive you" applied to all of Joseph's children, not just Joseph Smith III.

Mark Hofmann forged a document known as the The Joseph Smith III blessing, which falsely represented itself as a father’s blessing given by the Prophet Joseph Smith on 17 January 1844 to his son, Joseph Smith III, to the effect that this son was his appointed successor. (See Ensign, May 1981.)off-site

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Question: Did Brigham promise that Joseph Smith III would eventually take over the Church?