This passage refers to Alma telling the Anti-Nephi-Lehies the story of his conversion—namely, when the angel appeared to him and the four sons of Mosiah (as described in Mosiah 27). The earliest textual sources (𝓟 as well as the first three editions) read conversion. (𝓞 is not extant except for the final n in the word; the spacing between extant fragments is sufficiently large that either conversion or conversation would fit.) The 1841 British edition accidentally misread conversion (the 1837 reading) as conversation, which will in some sense work since Alma and the four sons of Mosiah had undoubtedly been conversing with each other (and the chief judge of the Nephites) on what to do to protect these Lamanites. But the larger passage argues against the word conversation. When Ammon returns with Alma, they first “made known unto them all these things”— namely, what the Nephites had agreed to do; their explanation would have included, at least by implication, any conversation Alma might have had with Ammon and the other sons of Mosiah regarding that issue. Thus when the text says that “Alma also related unto them ”, that information should be something new, like Alma’s conversion story (which was much more personal and harrowing than what the sons of king Mosiah, who were with Alma when the angel appeared, could have previously told the Anti-Nephi-Lehies about that experience).
The incorrect conversation was not easily removed from the LDS text. After its first appearance in the 1841 British edition, Orson Pratt restored the correct conversion in the 1849 edition. The word was, however, misspelled in the 1849 edition as convertion, perhaps because the copytext for the 1849 edition was a copy of the 1841 British edition in which Pratt, we can speculate, had corrected conversation to conversion by simply crossing out the sa in conversation, giving convertion (it would have been better to have crossed out the at). Another possibility is that the 1849 misspelling resulted from the fact that conversion is related to the verb convert, which ends in t. In any event, in the first printing of the 1852 edition, the word was spelled correctly as conversion, but for the second printing, the 1841 reading was intentionally restored to the LDS text. (The clear majority of the substantive changes for the second 1852 printing derive from the 1840 Cincinnati/Nauvoo edition, not from the 1841 British edition.) Finally, in the 1879 edition, Orson Pratt once more restored the correct conversion to the text.
As discussed under Mosiah 19:24 (with respect to the word ceremony), the Book of Mormon text never actually uses the term conversation, although there are eight examples of the verb converse. On the other hand, there are four other occurrences of the word conversion in the Book of Mormon text:
So the original use of conversion here in Alma 27:26 is perfectly acceptable.
Summary: Accept in Alma 27:25 the word conversion, the reading found in the earliest textual sources and the one that makes more sense contextually than conversation.