How do we account for fulfilled prophecies made by Latter-day prophets?

Joseph Bailey Smith born in 1870 was the grandson of Samuel H. Smith (brother of the prophet Joseph Smith Jr.). Part of a letter written on January 5, 1923 by Joseph Bailey Smith to his son Joseph Byron Smith reads:

My Son Joseph you are all I have from Effie [Field Howell] that will listen an not always make one feel bad I love you more than I can tell and my first blessing go to you, you will build the Lord work as did Samuel H Smith you shall have part in the construction of many Wards. You was bless by Joseph F. Smith. Prophet of the church, and when You and were in his office YOU was part of a REVELATION given when I spoke that it has to bad that the Abraham papyraham were burnt in the Chicago fire Joseph F. Smith put his hans to his face and said Bro Joseph they are not gon and before your son is 63 years old they will be in the hands of the Church. You will live to see this and you will know the truth. I have not seen Young <Joseph> tell truth. (emphasis added)
– Joseph B. Smith letter, Salt Lake City, Utah to Joseph B. Smith Jr., Lofgreen, Utah

In this letter Joseph Bailey Smith describes a prophecy by Joseph F. Smith given after a blessing from the prophet to Joseph Byron.

On November 27, 1967 this prophecy was fulfilled when the surviving fragments of the Joseph Smith Papyri were returned to the church just a few days before Joseph Byron Smith turned 61.

How would Joseph F. Smith have known this? Why would he be so specific in the prophecy?

See:

Stephen Smoot – A Fulfilled Prophecy of Joseph F. Smith

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