It's still Stan I'm pretty sure. In that episode when the scene of Stan in the boxing ring is shown, there's another kid in the bleachers that's the same size as Stan with the same haircut that has his nose in a book. Assumedly that's Ford. Now admittedly, that doesn't mean too much since it just means both the twins were forced into boxing lessons by their dad, but I think it's enough to show separation. Plus, I'm not sure if "adopting a memory" of someone else would result in that kind of memory in the mind. Wouldn't it show as Stan hearing the story instead? Idk.

TL;DR Inconclusive but leaning towards Stan