You most likely have no recourse: your neighbor would only be liable if both the following were true:1) The downspout is not just for her roof, but she actually owns or controls it, so she is the one who could fix, correct, move, etc. it if necessary. If she could not control the downspout, she is not liable for any damage done by it.2) She had knowledge of the damage that was being done, since without knowing there was a problem, there would be no reason for her to take action--and no liability for not doing so.