Major Themes of The Fifth Head of Cerberus

There are at least two major themes of tFHoC:

Consideration of the Turing Test

If a simulation could duplicate self-awareness -- sentience -- so perfectly that you couldn't tell the difference it and "authentic" sentience, would it be sentient?

The primary argument for the answer to be "no" is the Chinese Room. 
Imagine a translations machine. You write Chinese sentences on a card and on the other side it outputs English. Inside the box is a person. He doesn't speak Chinese or English but follows a series of complex rules for translating Chinese into English. By following the rules he simulates translation without ever understanding a word of either language. He's a non-sentient translator who passes the Turning test.

In the tFHoC, Wolfe supposes a simulated sentience that simulates a few levels deeper than that -- a simulation with a psychic ability to see into the inner workings of a mind and duplicate what happens there. 

Is it still a simulation? 

What if it can lose it its sentience if it is away from humanity for long enough. Its that sentience meaningful as long as it persists?

Colonization

What tFHoC is saying is quite simply this:
Colonists are colonized in turn by the people and lands they colonize. They are changed. The English, raised in India, who returned to England were no longer seen as "one of us". 

And this relates to Veil's Hypothesis:

“Veil’s Hypothesis supposes the abos to have possessed the ability to mimic mankind perfectly. Veil thought that when the ships came from Earth the abos killed everyone and took their places and the ships, so they’re not dead at all, we are.”  

“You mean the Earth people are,” my aunt said. “The human beings.”

John V Marsch follows this up with Liev's Post Postulate:

"I have read the interview with Mrs Blount-a hundred times while I was in the hills-and I know who I believe the Free People to be: I call it Liev’s Postpostulate. I am Liev and I have left."

John V Marsch never details what Liev's Post Postulate but it is easy enough to suppose. Remember it is a "post-postulate". Not an anti-postulate. It follows from Veil's Hypothesis. It is this:

If the Annese mimicked humanity so perfectly that they replaced humanity, then humanity has replaced -- over-written -- the Anneseness of the Annese. They are no longer what they once were and they can't go back. They've lost the ability change and they've lost the ability procreate. Over time, as more humans encounter Annese, the Annese will mimic them and be lost, leaving only a kind of human with out the ability to be become more.

The upshot of Liev's Post-Postulate is.... the Annese who replaced humanity have left -- they are gone.