Generally, Part II and Part III each uses its own suite of theme BGM (background music), but TVB, quite cleverly, occasionally used Part I's themes in Part II and Part III...especially during moments when Ding Lik reminisced about the past. There was a very touching five-minute sequence in Episode 4 of Part II when Ding Lik remembered a conversation he had with Hui Mun Keung a few years earlier, and the Part I theme was played. What was great about this scene is that it wasn't in Part I. Yes: Chow Yun Fat returned to film a new five-minute sequence for Part II that revealed a previously untold conversation between Hui Mun Keung and Ding Lik...one that proved prophetic about Ding Lik's current circumstances as of Part II.
Also, I previously was under the impression that Hui Mun Keung was never alluded to in Part III. As it turns out, in the very last episode of Part III, Ding Lik makes a very brief, but poignant mention of "Mun-gor" that shows us how mature Ah Lik had become by Part III. Hui Mun Keung would have been so proud of his old friend and sworn brother if he could have seen Ah Lik in Part III.