I agree I like to let them heal naturally IF POSSIBLE. Sometimes it isn't but mostly it is
. A split fin can be a split fin forever as said. Bettas get better really fast so if you don't notice it healing up within another week(about)I'd say the chance is it just won't get better sadly. Not to say the fishy can't live a happy life anyway! Keep on spoiling the little guy hehe.
One great thing for bettas if you haven't tried it is the indian almond leaves. It simulates the water bettas are in while in the wild. It helps them to get nice hard scales and I >THINK< helps speed up damaged fin growth.