James 5:19-20… has many different interpretations, but I believe the best is Dr. Criswell’s who says vv.19-20 are talking about the conversion of a lost sinner and thus saving the soul from hell.
Dr. Criswell said on January 12,1975 at FBC Dallas, Texas:
“The inspired pastor of the church at Jerusalem writes about,  not only the greatest tragedy when a soul is lost,  not only the greatest work that we win that somebody who is lost, but  look at the greatest blessing in 2 parts:
“19 My brethren, if any among you strays from the truth and one turns him back, 20 let him know that he who turns a sinner from the error of his way  will save his soul from death [eternal separation from Jesus A] and  will cover a multitude of sins” [James 5:19-20].
I think, in my studying and praying over the text, it refers to two things. I think it refers – if we win somebody who is deep in sin, not only is their soul saved but,  all of the sins of their life are covered over; they are hidden away.
The prodigal son, when he came back home the first thing the father said is, “Bring a new robe and put it on him. Hide those old rags and the marks of the pigpen. Hide them away. Put a beautiful robe on him” [Luke 15:22]. That is the way we are going to be in heaven, clothed in beautiful robes. I think it refers to that, a sinner who is deep in sin; God put the beautiful robe on him.
One time, I was locked up with a famous criminal in Alcatraz, in the Bay of San Francisco. He said to me, when I had done preaching, and testifying, and praying with him, he said, “The first thing I will do if I ever get out of this prison, I will walk down that aisle in your church, and I will confess my faith, and you can baptize me.” And after the years, when finally he was out of prison, he walked down this aisle here and confessed his faith before you, and I baptized him. “save his soul from death and will cover a multitude of sins” [James 5:20].” [Source: W. A. Criswell sermon notes]
And he who is wise wins souls. [Proverbs 11:30b NASB]
Notes: A- The first death is when the soul is separated from the body [2 Corinthians 5:8]; that is what the world calls death. The second death is when the soul is separated from God; that is “the second death” [Revelation 20:11-15], not the cessation of being or of existence, but being shut out from the presence of the Lord. And some of the words in the Bible, describing that separation, that state of exclusion, are sad and tragic beyond description. To be shut out from God, the estate of being separated from the Lord is called, “Living where the worm never dies and where the fire is never quenched” [Luke 9:48], “where there is weeping, and wailing, and gnashing of teeth” [Matthew 13:42], “where the smoke of their torment arises forever” [Revelation 14:11], where they cry for a drop of water that they might be somehow assuaged in the torment of that pain[Luke 16:24]. Oh, the sadness of one who dies away from God!