If my neighbor had a prescriptive right on my property, would that right transfer to new owners when that his property is sold?

The first thing you would need to do is confirm where your property line is and whether, in fact, the fence is encroaching on your property. If it is, it has remained there with your permission until now and your neighbor has not gained any rights to that portion of your property. Based upon your question, I assume that the fence is your neighbors. You can ask him to move the fence, if he doesn't, you can proceed to take action to have it removed. I would contact a local attorney to determine if you can "self-help" and take it down yourself or whether you must first obtain court approval. Good luck.

This is a complex area of law. Generally, a prescriptive easement does not exist until the court quiet's title to one. The same is true of the doctrine of adverse possession. The fact that a fence is one property or another is not dispositive of the issue. If the boundary is not disputed, then where the fence has been placed is truly irrelevant. If there has been no judgment quieting title to a prescriptive easement, then there is no prescriptive easement to pass. Subsequent owners may tack the prior use to prove up a prescriptive claim of their own, however. As I look at your post, however, I cannot tell whether you have a boundary dispute issue, an issue over placement of a fence, an adverse possession claim (which I doubt due to the requirement to pay property taxes), or a claim to a prescriptive easement (also rare and requiring use, along with other elements.) What is the exact issue here?

In my opinion, there is generally no right to a 'prescriptive' easement to maintain a fense as it would fence the fee owner out of their own land and be equivalent to an illegal subdivision in violation of the Subdivision Map Act. I suggest you consult a lawyer and put the new own on notice you are moving the fence on your property to the property line.