How does memory work among Horcruxes?

Question

At the time of Harry Potter and the Chamber of Secrets we have 2 conscious and functioning Horcruxes - young Tom Riddle from the Diary and the "main piece" hiding somewhere in Albania.

Young Tom Riddle reveals that he is not aware of the future - it's Ginny who told him that Voldemort was defeated when trying to kill Harry.

“Well, you see, Ginny told me all about you, Harry,” said Riddle. “Your whole fascinating history.“ His eyes roved over the lightning scar on Harry’s forehead, and their expression grew hungrier. “I knew I must find out more about you, talk to you, meet you if I could. So I decided to show you my famous capture of that great oaf, Hagrid, to gain your trust—”

[...]

“Haven’t I already told you,” said Riddle quietly, “that killing Mudbloods doesn’t matter to me anymore? For many months now, my new target has been—you.”

[...]

“So I made Ginny write her own farewell on the wall and come down here to wait. She struggled and cried and became very boring. But there isn’t much life left in her… She put too much into the diary, into me. Enough to let me leave its pages at last… I have been waiting for you to appear since we arrived here. I knew you’d come. I have many questions for you, Harry Potter.”

“Like what?” Harry spat, fists still clenched.

“Well,” said Riddle, smiling pleasantly, “how is it that you a skinny boy with no extraordinary magical talent—managed to defeat the greatest wizard of all time? How did you escape with nothing but a scar, while Lord Voldemort’s powers were destroyed?” There was an odd red gleam in his hungry eyes now.

_{— Harry Potter and the Chamber of Secrets, chapter 17, The Heir of Slytherin}

It is quite clear, that the Diary only has a memory of 16 years old Tom Riddle.

If he were to win that fight and consume Ginny, what would happen with his memory? What would be his memory state at the moment?
This question addresses whether there would be 2 Voldemorts and how would they interact. For the sake of this question, I set that aside and actually ask in what state exactly will Voldemort's memory be and why. I see three possible outcomes:

• The memory of Tom Riddle from the diary will merge with the original Voldemort's memory (though I'm not sure in this one since Voldemort doesn't seem to have any connection to his Horcruxes as he doesn't even notice them being destroyed)
• Riddle's 16 y.o. identity will dominate and be more or less single source of memory since that is Horcrux's condition
• vice versa original Voldemort's identity will prevail since he's the original one and have higher ground on this. He can't die while there's at least a single Horcrux, while Horcruxes can be destroyed, which places his original part higher.

Answer 1

They won’t re-merge if Tom ‘solidifies’.

Though it’s not clear exactly what Tom Riddle would do if he solidified, it is clear that he wouldn’t recombine with the Dark Lord’s soul, since the only known way of putting a soul back together after creating a Horcrux is by feeling sufficient remorse.

“Isn’t there any way of putting yourself back together?’ Ron asked.

‘Yes,’ said Hermione, with a hollow smile, ‘but it would be excruciatingly painful.’

‘Why? How do you do it?’ asked Harry.

‘Remorse,’ said Hermione. ‘You’ve got to really feel what you’ve done. There’s a footnote. Apparently the pain of it can destroy you.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 6 (The Ghoul in Pyjamas)}}

Without their creator feeling sufficiently remorseful, Horcruxes don’t just recombine with the main soul piece. Therefore, though Tom would be much stronger if he sapped someone’s life force, this strength wouldn’t cause him to combine with the Dark Lord.

They won’t share memory - they’re separate.

As Tom Riddle and the Dark Lord would remain separate, their memories wouldn’t be shared, since they never shared memories when Tom was less strong. It’s clear Tom didn’t know how the Dark Lord died in his future - he only knew what Ginny told him.

“Well, you see, Ginny told me all about you, Harry,’ said Riddle. ‘Your whole fascinating history.’ His eyes roved over the lightning scar on Harry’s forehead, and his expression grew hungrier. ‘I knew I must find out more about you, talk to you, meet you if I could.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 17 (The Heir of Slytherin)}}

It’s also clear that the Dark Lord didn’t share Tom Riddle’s memories, since he wasn’t aware of Tom’s encountering Harry or the diary being destroyed until he found out from Lucius.

“Perhaps, at the point of death, he might be aware of his loss … but he was not aware, for instance, that the diary had been destroyed until he forced the truth out of Lucius Malfoy. When Voldemort discovered that the diary had been mutilated and robbed of all its powers, I am told that his anger was terrible to behold.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)}}

There’s no reason to think this would change, and Tom Riddle and the Dark Lord would then share memories, if Tom gained strength by sapping someone’s life force and becoming more solid. Presumably their memories would remain separate and unshared, as they’d still be separate pieces of soul, since Horcruxes don’t recombine with the main soul without their creator feeling remorse.