Here Oliver Cowdery accidentally omitted the subordinate conjunction that when he copied the text from 𝓞 into 𝓟. The that is found at the end of the line in 𝓞, which probably explains why it was lost during the copying process. See under Alma 11:21 for a list of cases where Oliver sometimes made copying errors at the end of a line in 𝓞, when his eye would move too quickly to the beginning of the next line and he would omit or misread the line-final word in 𝓞.
Elsewhere in the text, whenever we have “for this cause” followed by a sentence acting as an appositive for the noun cause, we always get the conjunction that at the head of the sentence:
Thus the subordinate conjunction that should definitely be restored in Alma 55:19.
Summary: Restore in Alma 55:19 the original that which heads the sentence that acts appositively to the noun cause: “for this cause that he might not bring upon him injustice …” (the reading of the original manuscript).