Maliketh in Farum Azula

Do we have any proove that when Maliketh was always in Farum Azula ?

Because I have a little reflection that could explain the spear in Marika's body when we enter in the Erdtree.

Maybe he was send in Farum Azula after the shattering. When Marika's broke the Elden Ring, Maliketh become mad, wanted to kill Marika since she betray the greater will.

But Radagon or the Elden Beast beat him and send him in Farum Azula to keep Marika alive (they need her to maintain the golden order if I understand well).

So, when the Remembrance of the Black Blade talk about the treason, it's not about the part of the rune of death that has been stolen, but the shattering.

It would explain how the rune was stolen, because it look odd that the thiefs get access to Farum (generaly, when a PNG need to go somewhere, we need to get there first) and Farum is not a easy place to find.