"Ich bin da schon besser integriert als er."
"Yet" is usually used in negations, like "I have not done it yet". In affirmative sentences it would rather be "already". I am already better integrated there than he is. However, this word is not as widely used in English as "schon" is in German, so quite often "schon" is left without any particular translation.
I'm not a native English speaker either, just sharing my thoughts.