OK, Reedy, if you really want to do this, you will need to dig down and physically remove the root. There is no magical formula to make it disappear. Fortunately, with a fir tree, once that root is gone, it's gone forever. To keep others from causing the same problem later, dig a 50 cm deep trench next to your fence, and line the fence side with copper mesh--expensive, with copper prices as they are--which will kill the young roots that come in contact with it. very heavy plastic (32 mil) will also work somewhat, but may just direct roots down and under. Keep in mind that if his tree dies, a judge might decide that he is justified in suing you. My original hope was that you and your neighbor could go halves on a remedy that would work for both of you.

You are quite within your rights to take up the patio and cut off the roots to your boundary, but if you put down root killer you will kill the tree. Have you spoken to your neighbours about it?.