I want to build a fence adjoining my neighbors previously constructed fence but it would cross over into his property; what can I do to protect his rights in that property?

I am not a SC lawyer, but in most every state there are provisions for granting easements and licenses.  Both are rights to use another person's land for some purpose.  The difference is that an easement continues to survive when either or both parcels are sold, whereas a license is personal to the person given the right, and depending on its terms may either continue or expire when the person giving the right transfers the property.  It shouldn't be too expensive to find a local lawyer who can advise the two of you on which would best suit your needs and draw up a document under your state's laws to implements your intentions.