Here Joseph Smith deleted the repeated subordinate conjunction that in his editing for the 1837 edition. The repeated that specifically refers the reader back to the earlier “unto the fulfilling of the word of the Lord”. The previous after-clause (which begins verse 14) did not have a that before it since, as already noted under 1 Nephi 10:2–3, the text tends to avoid the sequence “that after that”. For additional discussion, see that in volume 3.
Summary: Restore the deleted subordinate conjunction that following “or in fine” in 1 Nephi 10:14; the that is used to help connect the text to the earlier reference in verse 13 (“the fulfilling of the word of the Lord”).