When Oliver Cowdery copied the text here from 𝓞 into 𝓟, he accidentally omitted desiring him. His eye seems to have skipped from the first him (“unto him”) to the second one (“desiring him”). But the 1830 edition reads desiring him, a clear indication that the 1830 edition was here proofed against 𝓞, not 𝓟 (as discussed more comprehensively under Alma 42:31). The 22nd signature for the 1830 edition was, however, set from 𝓟. In fact, there is proof in that manuscript that the 1830 edition was originally set to read “unto him that he should inquire”. When the compositor filled up his composing stick with type (from 11 to 13 lines of type), he would typically make a small cut in his copytext (here the printer’s manuscript) to show where he currently was in his typesetting. In Alma 43:23, this small cut in 𝓟 occurs after that he should (which is missing the words desiring him). But the actual printed 1830 edition ends the line with desiring him. This shows that originally the compositor strictly followed the printer’s manuscript (that is, his 12th line of type originally read “prophecies of Alma, sent certain men unto him that he should”), but in the process of proofing against the original manuscript it was discovered that desiring him needed to be added, so the words that he should were shifted downward into the next line (and at least some of the remaining lines in the paragraph also had to be shifted). In order to represent the position in 𝓟 of this particular cut mark, I insert a check mark (ƒ) into the two lines as set in the 1830 edition:
For further discussion regarding these cut marks in 𝓟, see pages 17–18 of volume 2 of the critical text (also see page 17 of volume 1).
Summary: Maintain in Alma 43:23 the participial phrase desiring him, the reading of the original manuscript.