There is a certain degree of variability from individual to individual but, in my experience, it's about 6-9 months for most parts of the face but less in dynamic areas (ie, the areas that move such as the lips and regions right around the mouth).
Complete dissolution may, therefore, take up to a year (if you mean every last molecule). From a practical standpoint, though, (and assuming there aren't any granulomas or scar tissue formation) it's about 6-9 months. And, of course, in some patients it lasts even longer.
I hope that this helps, and good luck,