Spoiler Alert: Kinda both. The Morgan from Faerie Britain has memories and knowledge from Proper Human History. That's why she knows what happen in both world, but the body is comes from Faerie Britain. This will explained at the main story.

@Muhammad Abdul Aziz Habibi I've already finish lb6, I know about the memories share thing. So the Morgan we have is the LB one which, because of the stuff that happens in Faerie Britain, has the memories of PHH Morgan. If so, I still don't think it makes sense that she antagonizes Saber(even though I like it a lot).

Thanks for the answer btw

Then I assumed you already know. You can see the Lostbelt's chronology for this, so you understand that Morgan comes from this LB and have knowledge from proper human history.