harry potter - How could Tom Riddle's diary know what happened between Tom and Hagrid?

It is said that Tom Riddle's diary was made into a Horcrux via the murder of Moaning Myrtle via Basilisk.

If that was the case, the soul piece that went into the diary was split off when this happened.

Yet, the diary piece of soul, somehow, showed Harry things which happened AFTER the murder - such as conversations about school closing with Headmaster and confronting Hagrid to frame him.

How could the diary-bound soul fragment know this?

Did Tom Riddle continue writing into the diary to keep that fragment updated? (that was the only plausible explanation I can guess at, since he was the only one who knew those scenes).

Answer

I have 2 options, the first of which, is that horcruxes do not need to be created at the exact moment you kill a victim. We know from JKR that there is a process and a spell or 2 that need to happen to create a horcrux, and we also know that killing damages the soul, which allows a piece to be broken off.

MA: What is the process? Do you-- Is there a spell? Is there a-- What do you have to do?

JKR: I see it as a series of things you would have to do. So you would have to perform a spell. But you would also-- I don't even know if I want to say it out loud, I know that sounds funny. But I did really think it through. There are two things that I think are too horrible, actually, to go into detail about.

Slughorn says,

‘By an act of evil – the supreme act of evil. By committing murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: he would encase the torn portion –’

So this process seems somewhat time consuming. We also know a damaged soul can only be repaired through remorse.

Ron: "Isn't there any way of putting yourself back together?" Hermione: "Yes, but it would be excruciatingly painful."

Harry: "Why? How do you do it?"

Hermione: "Remorse. You've got to really feel what you've done. There’s a footnote. Apparently the pain of it can destroy you. I can’t see Voldemort attempting it somehow, can you?"

So given this, we again don't have an exact date that he created the diary, but I would hazard that he created it AFTER he was told he could no longer stay at Hogwarts over the summer, and decided to close the chamber, and frame Hagrid. This to me is the most logical conclusion as the Diary was intended to be used to open the chamber again.

The second option which is a very simple fix to adding memories after the fact.

We know how easy it is for memories to be extracted in Harry Potter, and in fact the memories we see through the diary have striking similar feel to memories viewed through the pensive.

Once before, Harry had found himself somewhere that nobody could see or hear him. That time, he had fallen through a page in an enchanted diary, right into somebody else’s memory . . . and unless he was very much mistaken, something of the sort had happened again. . . .

This memory is the only one that Tom chooses to show Harry, and it may simply be because it is the only memory added to the Diary in a way which can be shown like this. So creating the Diary immediately after killing Murtle and then added the memory of catching Hagrid after the fact is a simple feat.