2.0 beta 10 cannot find user contributed library

This is incorrect. An Arduino library is a folder. That library folder must be installed under the libraries subfolder of the sketchbook folder.

So it would look something like this

<sketchbook folder>
|_ libraries
   |_ FSM
      |_ FSM.h
      |_ <other library files...>

There is an alternative "recursive" library format that is actually more common than the "legacy" format shown above:

<sketchbook folder>
|_ libraries
   |_ FSM
      |_ library.properties
      |_ src
         |_ FSM.h
         |_ <other library source files...>

Either format is likely fine for your application of a manual installation. I just didn't want you to be confused if you saw the different structure of some other recursive library you had installed.

Your #include directive is wrong. Change it to this:

#include <FSM.h>

The Arduino build system automatically discovers the library that contains the header file and compiles it. You should not specify the path to the file in your #include directive.