  We write the conditions for open strings with charged endpoints in the
language of gluing matrices. We identify constraints imposed on the gluing
matrices that are essential in this setup and investigate the question of their
invariance under the Poisson-Lie T-plurality transformations. We show that the
chosen set of constraints is equivalent to the statement that the lifts of
D-branes into the Drinfel'd double are right cosets with respect to a maximally
isotropic subgroup and therefore it is invariant under the Poisson-Lie
T-plurality transformations.
