So it's been established that when a human is 'turned' into a vampire, their soul departs and a demon moves in. So is the Angel we all know and love the demon, now saddled with a soul, or is he Liam returned?
Depends on how you look at it.
As you said in your question, "it's been established that when a human is 'turned' into a vampire, their soul departs and a demon moves in." But they also physically become a vampire, which you might consider a demon.
There is a distinction drawn, however, between the vampire itself and the demonic spirit possessing its body. A vampire itself is a sort of hybrid between human and demon. I believe that's why vampires can change from appearing human to "vamp face", and why they retain the personality traits of their human self.
An illustrative example can be found at the end of Angel season 2. Angel and friends find themselves in a dimension where Angel doesn't suffer from the normal vampire weaknesses - but when the demon take over, he looks complete demonic and acts purely as the demon dictates. Here's an exchange from S2E21 "Through the Looking Glass" that explains it:
WESLEY: Angel's vampire self has been sublimated somehow by this dimension. ... Only his human side has surfaced since we've been here.
GUNN: You mean, being able to walk around in the sun? Seeing his reflection. Like that?
WESLEY: Yes. And now, for whatever reason, he's accessed his demon, but he can't find the balance he normally would in our world. His demon self has totally overcome his human side.
GUNN: So that's what the thing inside of him really looks like?
WESLEY: In its purest form.
So Angel is Liam - he has all of the memories and personality he had as a mortal, as well as his soul. But he is also still the demon - he is still physically a vampire, and still has a demonic spirit trying to influence his actions.
Maybe look at it like this:
- Angelus = Liam - soul + demon
- Angel = Angelus + soul (seems like demon saddled with a soul)
- Angel = Liam + demon (seems like Liam returned)
Make of that what you will.
I think it depends on what you would consider "Liam" to be. Do you believe that a person's essence is a spiritual soul, or do you believe a person is the sum of their physical parts - making "Liam" a combination of genes, experiences, memories, environment, etc.
If it's the former, you could say that Liam never returned once turned. As I understand it, it was never established that Angel got "his" soul, just a "soul". Sometimes they say he got his soul, sometimes they say he got a soul. The specifics of having a soul and what a soul means are not very well-defined. At times it seems a soul is the ability to care about things that are not directly related to you - for example, vampires care deeply about the suffering of people they are invested in, but don't seem to care about strangers that are essentially food. I don't think there is an answer to this so we can't say for sure if "Liam" is in the soul Angel has.
However, if you believe in the latter theory, that Liam is a combination of genetics, environment, memories, etc., then Liam is always there. When he identifies as Angelus, he is Liam without a soul. When he is Angel, he is Liam with a soul. He still has all his memories, he is in the same body, more or less. How many changes must a person undergo and in what speed before they are not "them" anymore? That is an interesting philosophical debate all in itself.
Either way, the question of what you define as "Liam" will lead you to the answer of whether Angel is Liam and when.