James means that God will use the actions of this person to persuade the sinner to repent and be saved. But James speaks as if it were this other person who actually saved the sinner's soul from death. (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here "death" refers to spiritual death, eternal separation from God. Alternate translation: "will save him from spiritual death, and God will forgive the sinner for all of his sins" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
Possible meanings are 1) the person who brings back the disobedient brother will have his sins forgiven or 2) the disobedient brother, when he returns to the Lord, will have his sins forgiven. Sins are spoken of as if they were objects that God could cover so that he would not see them, so that he would forgive them. (See: [[rc://en/ta/man/translate/figs-metaphor]])