In this work, a new robust and fast method is developed to perform transfers that minimize fuel consumption between two invariant manifolds of periodic orbits in the circular restricted three-body problem. The method starts with an impulse transfer between two invariant manifolds to build an optimal control problem. This allows to choose an adequate fixed transfer time. Using the Pontryagin maximum principle, the resolution of the problem is formulated as that of finding the zero of a shooting function (indirect method). The algorithm couples different kinds of continuations (on cost, final state, and thrust) to improve robustness and to initialize the solver. The efficiency of the method is illustrated with numerical examples. Finally, the influence of the transfer time is studied numerically thanks to a continuation on this parameter, and it checks that, when transfer duration goes to zero, the control converges to the impulse transfer that it started with. It shows the robustness of the method and establishes a mathematical link between the two problems.