There is some minor variation here regarding inner versus inward and outer versus outward, in both instances with regard to the word vessel. The earliest textual sources favor “inward vessel” but “outer vessel”. Note that inward and outer do not match morphologically (inward and outward would form a matching pair as would inner and outer). The textual tendency, although minor, has been to create morphologically matching pairs. In the 1888 LDS edition, outer was replaced by outward in verse 23, thus matching the inward of the previous clause (“the inward vessel shall be cleansed first”). And in verse 24, we have some confusion in the printer’s manuscript, where Oliver Cowdery initially wrote “inner vessel”, which matches the “outer vessel” of verse 23; then later (perhaps while proofing against 𝓞, no longer extant here) Oliver corrected inner to inward with somewhat heavier ink flow. There would have been no motivation for Oliver to make this correction towards the morphologically nonmatching inward except that 𝓞 itself read inward. The critical text will maintain the corrected reading in 𝓟 for Alma 60:24, “inward vessel”.
The reference here in Alma 60:23–24 to God’s statement that the inward vessel should be cleansed first is similar to Christ’s words in the Gospels, which read as follows in the King James Bible:
Obviously, Moroni is not directly quoting Christ’s version, but the metaphor is the same. Further note that in the King James Bible the Matthew passage pairs outside against within while the Luke passage pairs outside against inward. Both pairs of words do not match morphologically and are in that respect like the Book of Mormon’s nonmatching outer and inward, although in Luke 11:40 there is the matching without and within. (In the Greek original, the pairs of words match morphologically. Similarly, modern English translations such as the Revised Standard Version and the New International Version consistently translate these word pairs as outside and inside.)
Summary: Accept the use of the morphologically nonmatching inward and outer in Alma 60:23–24, the reading of the earliest textual sources.