In MIB: International, it is revealed that
the real mole in the organization is High T.
What happened to him in 2016? Did he die, or did the Hive occupy his body? Or was he a Hive mutant all along?
Some visible spoilers in this answer!
At about 01h29m24s into the movie, on top of the Eiffel tower and adjacent to the wormhole (?) that M has just been thrown into, H is combating the hive/High T combined being hand-to-hand.
He is losing and appeals to the humanity remaining in the combined creature.
H pleads: You said I was like a son to you. You were like a father to me.
The combined creature hesitates.
High T: H ... (face morphs back to show some features of High T and the combined creature opens his clenched fist to expose the artifact)
Meanwhile, Pawnee has rescued M from the wormhole and pulled her back behind the fight. H grabs the artifact from the creature's open palm and tosses it back to M. She opens it up into its weapon form and fires at the creature.
There is also this comment from High T at about 0h47m25s during a conversation with H and M.
High T: The Diad's DNA is riddled with hive mutations. As we all know, the hive doesn't just destroy their enemies, they subsume them; take them over from within.
So it must be a combined creature with the hive creature usually dominating the human half until the human half struggles briefly to the surface.
As to when the combining occured, we aren't given much in the way of specifics beyond this comment from O in a conversation with H and M.
I hadn't trusted London branch in some time. I never understood the reason why. T lived for this organization; he was the very best we had. He will be ... missed.
So it seems that the battle in 2016 was the DNA subsuming event but that's not definitive beyond the fact that,
High T neuralized H and fed him an alternate version of the outcome of the 2016 battle with the hive. This was discovered when M called H on the fact that he repeated the outcome verbatim and without details.
This could be a variation of the Humanity Ensues Trope.