B. H. Roberts addresses the theory of multiple authorship of Isaiah in 1909: argues that the evidence from the New Testament and Book of Mormon supports the unity of Isaiah.
B. H. Roberts, “An Objection to the Book of Mormon Answered," Improvement Era 12, no. 9 (July 1909):681-89
It is held that Isaiah's historical period— the period of his ministry— runs through the reigns of four kings of Judah— Uzziah, Jotham, Ahaz and Hezekiah. Some extend his ministry over into the reign of Manasseh, by whose edict, it is said, he was sawn asunder. In any event Isaiah would be a very aged man at the reign of Hezekiah, 698 B. C; and he would have been between eighty and ninety at the accession of Manasseh. So that it is safe to say that his life ended soon after the close of Hezekiah's reign. Now if it be true that the latter part of the Book of Isaiah, from chapter forty to chapter sixty-six, inclusive, was not written until and during the Babylonian captivity, 586-538 B.C.— as is assumed by modern criticism— then of course the Prophet Isaiah did not write that part of the book which bears his name as author.
Again: If it be true that these chapters 40-66 were not written until and during the Babylonian captivity, then Lehi could not have taken that part of the book of Isaiah with him into the wilderness and subsequently brought it with him to America, where his son Nephi copied passages and whole chapters into the record he engraved upon plates called the plates of Nephi, since Lehi left Jerusalem 600 years B. C.
The difficulty presented by the higher criticism is obvious; viz., if Joseph Smith is representing the first Nephi as transcribing into his Nephite records passages and whole chapters purporting to have been written by Isaiah, when as a matter of fact those chapters were not written until a hundred and twenty-five or a hundred and fifty years after Isaiah's death; and not until fifty years after Lehi's colony had departed from Jerusalem; then Joseph Smith is representing Nephi as doing that which is impossible, and throws the whole Book of Mormon under suspicion of being fraudulent. This, therefore, becomes a very interesting as well as a very important objection; and many among the higher critics will say a fatal one . Here it can only be treated in outline ; it is undoubtedly worthy of exhaustive analysis.
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Believers in the Book of Mormon have no occasion of uneasiness because passages from the latter part of Isaiah's book are found transcribed into the Nephite record. The theories of modern critics have not destroyed the integrity and unity of the Book of Isaiah. And after the overwhelming evidences for the truth of the Book of Mormon are taken into account; and it is found that on the plates of Nephi there were transcripts from the latter part of Isaiah's writings, taken from a copy of his prophecies carried by a colony of Jews from Jerusalem to the western hemisphere, six hundred years before Christ— men will discern in this discovery new evidence for the Isaiah authorship of the whole book of Isaiah.