Which of these Enderverse characters died first?

Question

In Shadow of the Giant Peter sends an email to Valentine noting Graff's and Rackham's deaths:

I knew Hyrum Graff and Mazer Rackham very well before they died, and you treated them with absolute fairness.

However, in Ender in Exile Graff sends Ender an email including this:

The passing of your brother must have come as more of a surprise. He was young, but his heart gave out. Pay no attention to the foolish rumors that always attend the death of the great. I saw the autopsy, and Peter had a weak heart, despite his healthy lifestyle.

So who really outlived whom here? Or is some kind of time-travel going on?

Edit: Major spoiler from Xenocide:

"I thought I'd never see you face to face again," said Ender. "You died so long ago." "Never believe a rumor of my death," said Peter. "I have as many lives as a cat. Also as many teeth, as many claws, and the same cheery, cooperative disposition."

Answer 1

Graff actually lived for at least^[1] several decades more, putting himself in suspended animation.

This was covered in Ender in Exile, Chapter 21:

Ender cleaned himself up. Stasis left him with a sort of scum all over his body; his skin seemed to crackle just a little when he moved. This can't be good for you, he thought as he scrubbed it off and the skin protested by giving him little stabbing pains. But Graff does stasis ten months of the year and he's still going strong.

This was when Ender just wore up, 18 years after leaving Shakespeare colony, and arrived on Ganges.

And then, in Chapter 23, we see an old retired Graff reading about Ganges events from Valentine:

"Ah, Mr. Graff," said O'Connor, "that's the truth. I can never stay. But it's not for lack of will. I have a lot of houses waiting for me to bring them what I brought you."

"And we have nothing to say to each other," said Graff, smiling. No, laughing silently, his frail chest heaving.

Please note that Shadow of the Giant is 2005, and EiE is 2008, and Card's official policy is that later works trump earlier ones in case of discrepancy, as detailed here: What is Orson Scott Card's position on discrepancies between various Enderverse books?

SPOILER ALERT FOR LAST Ender BOOK!!!

_{[1] - There are rumours that based on the early non-public drafts of "Messenger" story (which may or may not be a first chapter of "Shadows Alive"), Graff actually lived - thanks to suspended animation - at least 3000 more years. Additionally, Peter is by then also "dead", in that Ender's auia now controls "New Peter"'s body, that got created during earlier books; so even if you count the "New Peter" as a person (despite no auia), Graff outlived him in absolute chronology}