“Can my neighbor be held responsible for their automatic lawn sprinkler that is overshooting to our property, and causing a moss buildup in our concrete fence that makes it ugly?”
First, have you spoken with your neighbor and asked them to adjust their sprinkler? If you have already tried this, and they have not cooperated, then you may want to consider sending them a registered letter explaining the damage being done to your fence, telling them that you are going to clean it, and that you would like them to cover the cost of the clean up. If they don’t reimburse you for the clean up, you may want to look into taking them to small claims court to cover your costs.
All that said, they are your neighbors, and you have to live with them. So weigh carefully whatever action you take and what the cost will be, and I don’t mean just financial.