  We lift the dynamical field of the $A_\infty$ superstring field theory to the
large Hilbert space by introducing a gauge invariance associated with the eta
zero mode. We then provide a field redefinition which relates the lifted field
to the dynamical field of Berkovits' superstring field theory in the large
Hilbert space. This generalizes the field redefinition in the small Hilbert
space described in earlier works, and gives some understanding of the relation
between the gauge symmetries of the theories. It also provides a new
perspective on the algebraic structure underlying gauge invariance of the
Wess-Zumino-Witten-like action.
