  We make use of an internal symmetry of a truncation of the bosonic sector of
the superstring and N=4 supergravity theories to write down an analogue of
Robinson's identity for the black holes of this theory. This allows us to prove
the uniqueness of a restricted class of black hole solutions. In particular, we
can apply the methods of the preceding paper to prove the uniqueness of a class
of accelerating black holes (the Stringy Ernst solution and Stringy C-metric)
which incorporate the possibility of the black hole accelerating within an
electromagnetic flux tube. These solutions and their associated uniqueness may
be useful in future instanton calculations.
