I'm wondering what exactly is shown to the Colonel by Griffin near the end of Men in Black 3 (MIB3)?
I don't remember exactly what the Colonel answered when J asked him what he saw, but it was pretty vague.
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He answers with
He showed me how important you are... you and your partner.
So my interpretation is he showed him the truth about J, J's future and his mission:
Young Agent K: You ever wanna see more, I know a top secret organization that can use a man like you.
Colonel: I wish I could.
Here I have the impression that Colonel has also seen his own death.
The film seemed to imply that he was shown clips from J's life; notice that he says J, specifically, is "important", then hastily amends that to being the pair of them. Similarly, he was probably aware that his death is what caused J to grow up as he had, since, as Guy pointed out, he seems aware of his own death.