At the juncture of verses 20 and 21 of 3 Nephi 19, Oliver Cowdery turned over his copywork to the unknown scribe 2, who then acted as the scribe for 𝓟 from 3 Nephi 19:21 to the end of Mormon. For this portion of the text, both 𝓟 and the 1830 are, from Helaman 13:17 to the end of Mormon, firsthand copies of 𝓞, but now we have to consider scribe 2’s scribal practice rather than Oliver Cowdery’s when evaluating 𝓟 against the 1830 edition.
Here in verse 22 of 3 Nephi 19, scribe 2 of 𝓟 wrote believd —that is, he wrote down the verb believe in the past tense. The 1830 edition, on the other hand, has the present-tense believe. The rest of the verse is in the present tense, including one more instance of the present-tense believe; we end up, then, with three present-tense statements, each of which ends in a because- clause in the present tense (at least in the 1830 edition):
The parallelism in the passage argues that the first believe should be in the present tense. In fact, in the second statement (listed above as 2) Jesus is explaining that the Father can see that his twelve disciples believe in him, Jesus, because he, the Father, can hear the prayers that they are praying while Jesus is praying, as explained just before Jesus starts his own prayer to the Father:
And, of course, the disciples had been baptized and received the Holy Ghost just before (described in verses 11–14), so here in 3 Nephi 19:22 the text is not referring to some remote event. The twelve had just received the Holy Ghost; thus the use in verse 22 of the present-tense believe (in fact, in both instances) is wholly appropriate. The critical text will retain the 1830 reading with its consistent use of the present tense in 3 Nephi 19:22.
We don’t have much evidence for a tendency on scribe 2’s part to replace the present tense with the past tense, although there is the following example from earlier on in his copywork (from Mosiah 25:14 through Alma 13:20, where he acted as the main scribe for 𝓟):
In this case, 𝓞 is extant and reads in the present tense: “I speak as though I had authority to command God”. Oliver Cowdery, when he later proofed 𝓟 against 𝓞, corrected scribe 2’s pasttense spake to speak. Scribe 2’s error in this other case may have been the result of the preceding perfect usage (“behold thou hast lied”) or the result of the past-tense subjunctive had that follows (“I speak as though I had authority to command God”). We note that here in 3 Nephi 19:22 there is a preceding perfect (“thou hast given them the Holy Ghost”) that could have prompted scribe 2 to write believed rather than believe in the immediately following clause.
Summary: Retain in 3 Nephi 19:22 the present-tense believe (the 1830 reading) since the entire verse is in the present tense; parallelism between the three statements in the verse argues that the presenttense believe is correct in “because they believe in me”.