The usual drill is that when you are coming off a long distance train, you can use the same ticket for traveling S-bahns in the arrival city on the day of arrival. Therefore, I would assume that you have not paid extra for the S-bahn part and it will not be valid on any other day. If you buy a ticket locally you have to validate it by stamping it in a machine before you get on the train or it is the same as note having a ticket. If your present S-Bahn ticket is undated then all you have to do is stamp it. If it is on the same page as the long distance route, don't use it the next day.