One advice, please don't expose him to any environment where someone would potentially point out his stammering and make him feel uncomfortable about it. Because it has happened to me in my childhood where my relatives would always give advices on how to talk or point it out, in the end, it made things even worse. Let him be fully comfortable and express himself, NEVER COMPLETE HIS SENTENCES. Wait for him and make him feel absolutely normal. Rest you are taking the right steps, in most cases it would just go away as he develops, just make sure he doesn't feel uncomfortable with his speech because that lingers in your brain an causes further damage.