  In this article we investigate the relation between consequences of Dirichlet
boundary conditions (momenta noncommutativity and parameters of the effective
theory) and background fields of fermionic T-dual theory. We impose Dirichlet
boundary conditions on the endpoints of the open string propagating in
background of type IIB superstring theory with constant background fields. We
showed that on the solution of the boundary conditions the momenta become
noncommutative, while the coordinates commute. Fermionic T-duality is also
introduced and its relation to noncommutativity is considered. We use compact
notation so that type IIB superstring formally gets the form of the bosonic one
with Grassman variables. Then momenta noncommutativity parameters are fermionic
T-dual fields. The effective theory, the initial theory on the solution of
boundary conditions, is bilinear in the effective coordinates, odd under
world-sheet parity transformation. The effective metric is equal to the initial
one and terms with the effective Kalb-Ramond field vanish.
