As for the rest of the acts of Solomon—all that he did, as well as his wisdom—are they not written in the Book of the Acts of Solomon?
We have here the conclusion of Solomon's story, and in it, 1. Reference is had to another history then extant, but (not being divinely inspired) since lost, the Book of the Acts of Solomon, Kg1 11:41. Probably this book was written by a chronologer or historiographer, whom Solomon employed to write his annals, out of which the sacred writer extracted what God saw fit to transmit to the church. 2.
Commenting on 1 Kings 11:41-43
And the rest of the acts of Solomon, and all that he did, and his wisdom, [are] they not written in the book of the acts of Solomon? (t) Which it is thought was lost in their captivity.
The book of the acts of Solomon? - These acts were written by Nathan the prophet, Ahijah the Shilonite, and Iddo the seer; as we learn from Ch2 9:29. Probably from these were the Books of Kings and Chronicles composed; but the original documents are long since lost.