We consider to apply the preconditioned conjugate-gradient method to a convergent sequence of symmetric and positive definite linear systems with multiple right hand sides where preconditioning is achieved by using the Limited Memory Preconditioners (LMPs). The LMP for each system matrix is obtained by using directions generated during solving the previous linear systems. These linear systems can be equivalently solved by using a dual approach, which can yield gains in terms of both memory usage and computational effort. A dual-space counterpart of the LMPs generating mathematically equivalent iterates to those of the primal approach is derived. After briefly presenting the particular LMPs such as the Ritz LMP, the spectral LMP and the quasi-Newton LMP for the dual approach, we focus on the quasi-Newton LMP and analyze its properties. Numerical experiments are finally presented using a toy problem based on a data assimilation system.