Huck attempts to save their lives because they are human beings regardless of being human beings who have murdered others. He also wants to make sure they survive so he can lead the authorities to them in order to make sure they are punished for their behavior.
What this tells us about Huck's character is that he is genuinely a fine individual. Although he is not "civilized" as the widow would like him to be, he is a person of incredible moral fiber. The lessons he learns on the river with Jim leave the reader with confidence that Huck will grow into the kind of adult male citizen that every one of us would like to have as a neighbor. He is fair, generous, kind, and honest. These are qualities that can not always be learned from books, and that many rationalize away when it benefits their own cause. We can be sure that Huck will not compromise his standards as he states quite bluntly that if allowing Jim to remain free will cause him to go to Hell, then he will just go to Hell.