This makes sense me only if he owns two jackets and has left the better one at the club. Like, he's leaving home and puts on the lesser jacket, leaving someone to explain "He has the better one at the club (as in, not here)."
In English, this is only grammatically correct if there are two jackets in the club. Otherwise you must use "best." Is German different or the same? Does "bessere Jacke im Verein" imply there are only two jackets in the club, and if 3+ then "beste"?