I trained for 3 years in Tang Soo Do as a teenager and achieved the rank of Cho Dan Bo. (black belt candidate) That was 35 years ago. 10 months ago, I started training in Tae Kwon Do. My school practices the ITF forms, which are similar, but not identical to the Pyong Anh forms I learned years ago back in my Tang Soo Do days.
So because of the long hiatus and because I was starting a new martial art, I started over as a white belt. 10 months in, I am a purple belt currently. That is somewhat more quick than usual, but not unheard of. I have gone past several people who were ahead of me, but there are people just a few months behind me who are also moving up fast. I think it all comes down to how much you commit yourself to training. I go 3 to 4 times a week. I think the people I went past either go less often, like once or twice a week or have taken some time off, and hence have not advanced as quickly as they might have otherwise.
The kicks, blocks, stances, and movements are mostly the same but not identical. While the front stances are the same, my current school likes a somewhat wider and longer back stance than did my former school, at least on forms. (fighting is whatever works best for the individual) My current school actually has more contact in sparring than my former school did, but we are all padded up, where as in my former school, there was minimal or no padding so when you got hit, you felt it more. Except for the forms, the rest of the curiculum is almost the same.
If your son has 9 years experience and earned a green belt in TSD, I see no reason why he shouldn't get to the equivalent rank at a TKD school reasonably quickly. That said, a lot depends on your son, and how good he really is, and how quickly he can learn the new forms. I have seen kids from other schools get moved up quickly at my current school, and other kids actually get demoted because despite their years of experience, they struggle with our curicullum. As for myself, I think my experience with TSD has mostly served me well. It is sort of like learning a foreign language, than learning another foreign language that is similar, but not identical.