In this passage we have a possible ambiguity with respect to Moses: should this name be interpreted as a subject or a possessive form? The presumable reading here is that Abinadi’s face shone just like Moses’s face shone, as indicated in the biblical text (although the King James Bible specifically refers to the skin of his face shining):
But since in Mosiah 13:5 the name Moses is not followed by any noun, one could theoretically read the text here as saying that Moses’s whole being shone, not just his face. In accord with the biblical reading, the critical text will accept the possessive form Moses’ as the correct reading.
Here in the printer’s manuscript, Oliver Cowdery originally wrote Moses without any apostrophe, but later he (or maybe Joseph Smith in his editing for the 1837 edition) added the apostrophe with heavier ink flow. The 1830 and the 1840 editions set Moses without any apostrophe, while the 1837 edition supplied the apostrophe. Two other editions have omitted the apostrophe (the 1858 Wright edition and the 1888 LDS edition), but all others (including the current LDS and RLDS editions) have the apostrophe.
The expanded possessive form Moses’s does not occur here or elsewhere in the Book of Mormon; there is only one other relevant passage with the possessive form of Moses, and it twice reads Moses’:
The critical text will therefore accept the possessive form Moses’ rather than the alternative Moses’s.
Summary: Accept the possessive form Moses’ in Mosiah 13:5 (“even as Moses’ did”) since the biblical text refers only to Moses’s face shining, not his whole being; the manuscript spellings consistently support the possessive form Moses’ over Moses’s.