I WILL ALSO SUGGEST YOU TO TAKE INTO CONSIDERATION HOW MANY YEARS YOUR NEIGHBOR HAS HAD THIS ARRANGEMENT. PROBABLY FROM BEFORE HE BOUGHT THE HOUSE NEXT DOOR. UNLESS YOU CANNOT FIT YOUR CAR IN THE DRIVEWAY, I WOULD RECOMMEND YOU LEAVE THINGS AS THEY ARE. YOU DON'T WANT AN ANGRY NEIGHBOR LIVING NEXT DOOR UNLESS YOU HAVE NO OTHER CHOICE, OR YOU MOVING OUT IN THE NEXT YEAR. NEIGHBOR FEUDS CAN ONLY BE RIVALED BY SIVORCE, BUT IN THAT CASE YOU NO LONGER HAVE TO LIVE WITH THE PERSON. IF ONE OR BOTH OF YOU HAVE CHILDREN IT CAN GET EVEN UGLIER AND IT IS JUST NOT WORTH IT. GOOD LUCK WHATEVER YOU DECIDE.
And you'd be responsible for putting up the new wall. (Presumably the new wall would be at the edge of your property. You'd have no right to build anything on your neighbor's property.)
And you'd be responsible if there were any negative consequences--such as some of your neighbor's property collapsing because it lacked sufficient support.
You might want to talk to your neighbor about this--about your plans and possible cost-sharing.
Also, talk to a real estate lawyer who can advise you on the issues covered above.
Hope that helps.
You could also start by calling the title company or survey company that performed the survey to see what they say.