As shown in the picture my neighbor's fence is already in place (the vertical fence) Mine will be horizontal and I need to set the post as close as possible to his. My post will support a gate (72" long) 

His post (white) is  already rotten and it is moving. 
What options do I have? How do I dig a hole next to his post (set in concrete) 
[![enter image description here][1]][1]

I don't think that his post will be enough to support everything. One option will be to extract his post, to replace it and to add a new one for myself and bury them both together in a large hole. Would this work?

  [1]: http://i.stack.imgur.com/jfs6I.png