My question involves real estate located in the State of: New Jersey

We just purchased a house and would like to replace the existing chain link fence with a new fence and put the new fence just inside the correct boundary line as per our survey. We had a survey done which shows our current fence is around 3.5 feet inside our property line. We know it's our fence since it wraps around and attaches to the sides of our house. However, we do not know when it was built. We mentioned our plans to our westerly neighbor, who said the house was owned solely by his wife and we would have to speak to her. They don't live in the house, they rent it out to a group of younger kids, and only stop by from time to time.

It's been two weeks since that conversation, and we hadn't seen his wife (we wanted to discuss with her in person), but just received a two page typed "Letter of Intent" from her in the mail saying she had spoken with her husband about our plans and told us to refrain from doing anything to the boundary line until she consults her lawyer. She doesn't want us to put up a new fence, nor trim any of the existing overgrown shrubbery that would be required to trim in order to build a new fence. She is claiming she has all the documents required to prove she is the rightful owner of the property from her side of our fence to the official survey line (and township border line) by virtue of adverse possession. She has owned the house since 1998 (in NJ the statute is 30 yrs), but says the fence was there when she bought the house.

We think she may just be trying to intimidate us into submission, which isn't going to happen, as we want to improve the property aesthetically and plan to resolve this legally if she forces us into it. (We prefer to resolve amicably but she already crossed that bridge by serving us a letter without speaking to us...) For what it's worth, the friendly neighbors on the easterly side have no issue with our plans, and they and other neighbors who have been in town for 30+ years do not know the woman who is contesting us other than a few less-than-pleasant run-ins throughout the years. It is a quaint seaside community where many neighbors have known each other over generations, and we've already made a lot of friends. Unfortunately, our westerly "neighbor" is not one of them.

The questions we have are:

1. Does adverse possession apply if it is clearly our fence? Does she have to prove the fence has been there 30+ years? And if she can, does her case have legs?

2. Her letter told us not to trim any shrubbery along the boundary line until the matter is resolved. Can she actually hold us to that if it's our property and on our side of the fence?

3. If we remove the fence (without putting a new one up), could we be punished for doing so after her letter asked us not to touch anything along the boundary? Meaning, would it look like we were acting in bad faith by doing so after receiving her letter?

Any other advice would be very helpful.