The original text here has a mixture of clausal forms. The clausal complement to the verb suffer begins as a that- clause (“that the records …”) but ends as an infinitival clause (“to fall into the hands of the Lamanites”). The two intervening relative clauses make this conflation of clausal types less noticeable. The editors for the 1920 LDS edition removed the that, thus substituting a complete infinitival clause for the original mixture. Here is another example of this kind of mixed clausal structure that was removed by editing (in this instance by Joseph Smith in his editing for the 1837 edition):
In this case, the mixed clause was made into a complete that- clause by emending to be to is. Similarly, here in Mormon 6:6 the editors for the 1920 edition could have replaced the infinitival to with, say, should:
For another example where the that was removed, see under Moroni 4:1. The critical text will, of course, restore the original mixed construction here in Mormon 6:6 as well as in 1 Nephi 1:3 and Moroni 4:1.
Summary: Restore in Mormon 6:6 the original mixed clausal complement that begins as a that-clause but ends as an infinitival clause.