Compiling
  B b = new B() { static final int x; };
gives error
  inner classes cannot have static declarations

but they can, provided the static declaration is a compile-time constant field (JLS8.1.3):
  B b = new B() { static final int x = 1; }; // Compiles OK

(I'll update the JLS to say "unless they are constant variables (4.12.4)" rather than "compile-time constant fields (15.28)".)