Instead of comin' over and being "the american" (what all people are called in Asia), he actually made an effort to integrate.

There's no appropriation here. He's what all expats should strive to be.

Appropriation is when you take something (often by deceit, lies or force) and (this is the important part) call it your own.

Had he for instance learned Terenggaun food, clothing, habits, or any part of the culture, returned to the UK and announced all of it as something he came up with, that would be cultural appropriation.

OTOH, what he has done -- given himself up to it ("I'm more Malay than English.") would be described, as why-oh-why points out, cultural integration.