For starters, *definitely get a survey -- it'll cost, but you do not want title problems at settlement, especially if you are on a typical subdivision lot. Get the survey before time slips by, and your wife's screening hedge hinders the ability of a surveyor to accurately locate the posts.
Here's how it works ... neighbor X (aggressive and uncooperative, as proven already, by building a line fence, this high no less, without consulting you and going in with you on the survey *required to accurately locate an expensive new fence) builds a fence one d4mn lousy foot inside your property line, meaning that you now have possession of say 124-feet of your platted 125-foot lot (for example).
15 years go by (time depends on state, NY is 10 yrs, VA 15 yrs, etc. and then your neighbor gets a survey to fix the date of possession and the location of his possession -- but as a sign of his aggressive cruelty, he does not file a suit to "quiet title" in his favor. Indeed, he may not have met (or he *may have met -- irrelevant) all the legal conditions to have successfully adverse possessed you. He just sits there.
Meanwhile, you are sucked into cooperating with him. First, you acknowledge the existence of the fence, and you build a visual screen which honors the fence and etc.
Then time goes by, and you need to sell your home, and its 125-foot lot. In your contract for purchase and sale, you will basically agree to show up at the settlement table with "marketable title" on a house on a 125-feet of lot in Subdivision Happy Acres, or whatever.
Your purchaser will need a survey, to see if there are any encroachments and etc. and the survey will show the old fence, and that you have clear title (possession) on 124-feet, and that you have a "title problem" on 1-foot, which on rural property is insignificant, but on a platted subdivision lot, defnintely is not. (0.2' fence encroachment may not be significant-- today--but do not think that adverse possession is a thing out of the past, or that is doesn't pertain as a *legal device* for trouble making on suburban lots.
Settlement date arrives, and you and the purchaser appear at the settlement table. The purchaser is ready with the cash, so he's all set, but ... he then demands that you make good on your end of the purchase and sale agreement. "You promised in our agreement for sale, to deliver clear and marketable title on 125 feet of lot width. My survey here says you are delivering clear and marketable title on only 124-feet. I demand that you make good on your contract, and get a quit claim deed from your neighbor, clearing up title on the 1 foot strip." Your wife freaks --- "You mean we have to get our neighbor's signature on a quit claim deed, in order to clear up a title problem on our 125-foot lot?" The purchaser may not be a heavy hitter, with a flock of lawyers on his payrole. But, the purchaser may also be working with your aggressive neighbor, to shake you out, since you may not have the cold cash needed to feed lawyers and defend yourself in a lengthy suit for specific performance, or you may not have legal standing, to file your own suit to quiet title on the adverse possessed area, and get your lot legally replatted down to 124 feet so you can sell clear title on the remaining 124 feet.
In effect, you are basically about to be "shaken out" of your property. It would not be the first time this has happened.
By confiscating only 1-foot on your property, and by not filing suit to quite title in his favor, your neighbor has just effectively confiscated your ability to contract to deliver clear title at a settlement table for the entirety of your 125-foot lot.
Seems unfair ... not really. The banks expect, and the courts want, land owners to defend the title their own land, including 125 foot lots.
Your neighbor's fence should be "setback" onto his side of the property line, enough that he can maintain both sides of the fence, without encroaching onto your "quiet enjoyment" of your property. Typically, the outside of the fencing posts should be set 0.25'-0.33' (3"-4") back from the property line, and the fencing barrier, e.g. the wire fabric, wood slats, chainlink, etc., projects out 1" or so. On a 4x4 post, this puts the center of the post at 1/2-foot back from the PL.
Ask your surveyor "tabluate each fence post" on his survey. That is, before you screen it off, he should locate the outside-midpoint of *each fence post, and create a table of "down and overs" for the fence. (11.56' down from the front NE corner, over +0.25' -- + being on your neighbor.) His survey should not just depict a fence, x--x--x, "somewhere" along the PL, with a few random "offsets" shown.
Not fun. Serious business ...
P.S. also, don't put up such heavy screening, that in 10 years time, the neighbor can move the fence when you are on vacation, without your knowing it. One of the neighbors tried to do that to my parents, and I had to wait until they went on vacation to put it back ... and had to remove all the screening to do it. That's another war story.