I am a native English speaker. The English is WRONG. You cannot say "he IS an important job"! He HAS an important job is correct- or (very formally, do not learn it)" "His is an important job"

Maybe I am wrong, but the sentence "His is an important job" seems grammatically incorrect to me(

I don't get that one. ...Is the meaning: "His job is important"? As the job is important for him, or he is important in his work?

I think the English is correct, it just is an archaic way of of saying things. Think of it as a rather formal and traditional way of speaking. Imagine someone giving a puffed-up speech: "Hers was a face worth a thousand ships"; "Ours is a country worth fighting for".