Stable Quasi-Satellite Orbits (QSOs) have gained a lot of attention as suitable candidate orbits to explore remote planetary moons. Despite many studies on QSO and its orbital stability are found in literature, the problem of efficient transfer between two QSO is still unsolved. Previous works on transfers between two QSOs includes transfers between planar QSOs using impulsive maneuvers and utilizing the bifurcated multiple-revolutional periodic QSOs (MP-QSOs). Purpose of this paper is to explore the three-dimensional case and design transfer trajectories from lower altitude QSOs to three-dimensional QSOs being considered for upcoming sample return missions like Martian Moons eXploration (MMX) and PHOOT-PRINT. Specifically, we utilize the unstable 3D QSO to generate manifolds and connect them to the planar QSO in the framework of Mars-Phobos Circular Hill Problem with Ellipsoidal secondary (HPE). Numerical simulations suggest that transfer between a planar and spatial QSO around Phobos is possible with ∆V as low as 8.277 m/s with TOF of 4.19 days and similarly transfer between a spatial and planar QSO with ∆V of 8.286 m/s with TOF of 6.75 days. As a result, transfer design space between planar and spatial QSOs is established using the invariant manifolds.