try a piece of mending plate( a connector that looks kinda like metal pegboard) about 2x5 inches,bent in the middle to match the angle of your connection. fasten to the topside of your parts to butt-splice them together. 1/2" prick point or self drilling sheet metal screws, any longer may catch debris on the points. then wrap the seam careful and tight with metal tape. paint to match your downspout, last for years.