We show that the classical S-matrix calculated from the recently proposed
superstring field theories give the correct perturbative S-matrix. In the proof
we exploit the fact that the vertices are obtained by a field redefinition in
the large Hilbert space. The result extends to include the NS-NS subsector of
type II superstring field theory and the recently found equations of motions
for the Ramond fields. In addition, our proof implies that the S-matrix
obtained from Berkovits' WZW-like string field theory then agrees with the
perturbative S-matrix to all orders.Comment: 19 pages, 2 figure