To trace the moral development of Huck, it is probably best to start with Jim. At the beginning oif the novel, Jim is not Huck’s friend; he is a slave. Huck understands this on some level, but as long as he can bug Jim and get him to talk about the hairball or tell fortunes, Huck does not think about him. When they meet on the river, Huck is lonely and he is glad to travel with Jim, even if Jim is a runaway slave. In many of the scenes on the river, you can see that Huck has an inner conflict about turning Jim in. In the meantime, he acts as a teacher to Jim at times, and they discuss religion and other deep subjects.
Huck learns as they go along, and this is important. He learns that Jim is his friend and that, deep down, he does not want to turn him in. Jim is always there for him, even though Huck does not treat him the right way. A key scene to show his growing maturity would be the scene in which Huck leaves the raft, then returns to trick Jim. Jim scolds him, and Huck decides to apologize, even though he feels he should not have to. This moment is the beginning of Huck’s maturity. It will assist him, later on, in refusing to betray his friend.
I would look in Chapter 2 for how he initially treats Jim, Chapters 8 and 9 should be helpful for the original part of the raft trip. Chapter 9-13 should contain some quotations to assist you.