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Someone as old and presumably experienced as Achilles could have continued to imbue Connor with knowledge long after the physical training was done. I think there has to be some form of cut off point where one decides to just let Connor go on his own and learn things on his own rather than passing down everything Achilles knew. Narration made it clear that he trained Connor in both physically and mentally; if there was anything that indicated that Connor was lacking knowledge, I think that falls on his own incompetence rather than being poorly trained.