thank you for the replies on this holiday, this issue is clearly preoccupying my enjoyment. jk, sorry i missed these questions, responses below:

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were you aware of the fence being set off from the property line as it was?
is there a requirement fences be set off from a property line any specific distance?

has the neighbor acted as the area on their side of the fence was in fact theirs?

has anybody spoken about where the property lines are at any time prior?

as to her owning the property less than 30 years:

the courts of new jersey have ruled that for a current possessor to be allowed to tack the time of a prior possessor, the prior possessor must have also met the requirements of adversely possessing the property so;

any idea how the prior owners thought of the issue?
Yes, we were aware when we bought it, but we didn't really think about this scenario playing out. We assumed when we wanted to replace the fence, we would inform our neighbors and hoped it wouldn't cause more than an annoyance at most on their part. Definitely didn't expect to be slapped with a lawsuit threat at a casual mention! This is our first house, perhaps naivete on our part not to anticipate this before closing.

Our town has no setoff requirements for fences.

Yes the neighbor is acting as if it is theirs. It's only a few feet, so it consists mainly of shrubbery on both sides, and some plants. They have not built any structures. Like I said, they rent it year-round and only stop by occasionally. We've owned the house 8 months and my husband saw them once when I wasnt home, and then we both spoke with the husband two weeks ago - I have never met the woman myself. The husband actually came to our house to thank us for informing them of and fixing a burst pipe at their house this past winter. The good neighborship is clearly not being reciprocated!

When my husband met the couple briefly this past winter, he mentioned the property line and wanting to put up a new fence eventually, as well as cutting down some rotting trees on their side of the fence, but within our property line. The husband acknowledged our property line and said it was ok with him, but the wife mentioned at that point she felt the trees were "grandfathered in" - so I believe she was asserting her belief of adverse possession at that time. It wasn't until we brought it up again two weeks ago that we got served the letter from her, though. The letter also clearly states that the property is solely hers and is not owned by her husband (which we looked up in county records as being true).

No idea what the previous owners thought of the situation and how they were using the property. Our other neighbors said it was a really nice family living there, though, and that it was a shame that it was sold to a landlord who rents it out to loud, partying youngsters, not to mention both her and her husband and adult daughter seem to all have had altercations with neighbors in the area. Our property has changed hands every few years for the past 20 years or so, so don't think there's been any consistency on our end.

Hope that helps, and thanks again.