Spacing between extant fragments of the original manuscript indicates that Oliver Cowdery probably wrote “or burial” initially in 𝓞 (that is, without any repeated his). But the printer’s manuscript reads “or his burial”. There are therefore two possibilities for the transmission of the text here:
(1) Oliver Cowdery missed the his when he initially wrote down the text in 𝓞, but then he corrected 𝓞 (perhaps immediately) by inserting the his supralinearly;
(2) there was no repeated his in 𝓞, but Oliver Cowdery accidentally added it when he copied the text into 𝓟.
There is independent evidence in 𝓟 that Oliver Cowdery could either omit or add the repeated his, at least temporarily:
It should also be noted that in Alma 45:18 the 1830 sheet (the 22nd signature) was proofed against 𝓞, which argues that the his was in 𝓞, even if supralinearly inserted. Yet even in this situation we must keep in mind that an intrusive his added in 𝓟 and set in the 1830 edition could have been left unchanged despite proofing against 𝓞. Consider, for instance, the phrase “the army of” in Alma 43:41, which was lost in copying from 𝓞 into 𝓟 and thus omitted when this passage was set for the 1830 edition. In this case, the phrase was not restored to the first edition, despite the proofing of the 1830 sheet against 𝓞.
Elsewhere in the text, when death is conjoined with another noun, the determiner his is typically not repeated:
Here we have five examples, one of which is in the very next verse following Alma 45:18 (and refers to the same subject, Alma’s death and burial). Nonetheless, all five of these examples involve the conjunction and rather than or. In two other cases involving his in noun phrase conjuncts conjoined by or, we get one case of repetition and one without:
In the second case, the or is used to conjoin different objects (“his tool” versus “his sword”). In the first case, on the other hand, the or refers to a semantic equivalence between the words dream and vision (“his dream or vision”). This difference implies (although the evidence is meager) that in Alma 45:18, since “his death” is not equivalent to “his burial” and the conjunction is or, the his can be repeated. This semantic analysis thus supports the reading in 𝓟, “his death or his burial”, but only weakly.
In any case, the 1837 edition omitted the repeated his in Alma 45:18. This change seems to be unintended. For another case where the 1837 edition accidentally omitted the repeated his (from the conjunctive phrase “all his gold and his silver”), see under Alma 15:16. In neither case was the 1837 deletion of the repeated his marked in 𝓟 by Joseph Smith. In any event, the fact that the 1837 edition omitted the repeated his here in Alma 45:18 supports the possibility that Oliver Cowdery initially omitted it in 𝓞. Since either reading is possible, we follow the earliest extant reading, namely, the one in 𝓟: “as to his death or his burial”.
Summary: Restore the repeated his in Alma 45:18 (“as to his death or his burial”), the reading of the earliest extant source, the printer’s manuscript.