Will we still have well water rights after my mother's property has been sold?

I don't understand why this is posted on the Foreclosure Defense page. But, what you claim to have is called an appurtenant easement. If your mother, or a previous owner of the property, duly conveyed and recorded a deed granting the easement to you, then all subsequent purchasers take the property "subject to" the easement, meaning they have to honor it. The only possible problem I see is that the "letter" filed in the registrar's office might not meet the legal requirements of a valid deed. You should have the document reviewed by an attorney experienced in real estate law. If everything is in order, then you should make sure your new neighbors are aware of the easement so they don't inadvertently do something to interfere with it. When they bought the property, they no doubt did a title search, which should have turned up your easement. One purpose of recording deeds is to give notice of this sort of thing to potential buyers so they can take it into consideration in deciding whether to buy.