Abstract China’s Chang’E-4 (CE-4) probe has started its exploration on the far side of the Moon thanks to the relay satellite---Queqiao---which is around the Earth-Moon collinear libration point $L_2$ and provides continuous communication links between the lander and ground stations. The triangular libration points of the Earth-Moon system, $L_4$ and $L_5$, have long been considered as potential locations for future space applications. As a possible extension of Queqiao or other future missions around $L_2$, the work presented here contributes to constructing transfers from the collinear libration point ($L_2$) to the triangular libration points. Taking the $L_4$ point as an example, two types of two-maneuver transfers from a planar Lyapunov orbit around $L_2$ to the periodic orbit around $L_4$ are investigated in the planar Earth-Moon system and compared with each other, including the type-I transfer utilizing invariant manifolds along with powered lunar gravity assist and the type-II transfer using the Jacobi integral. Our studies indicate that type-I transfer saves more $\Delta v$ cost than type-II transfer. For the cases studied by us, the minimum $\Delta v$ cost is about 0.1636 km/s for type-I transfer, with a corresponding transfer time of 169.84 days. For type-II transfer and the cases studied by us, the corresponding values are 0.4745 km/s and 137.19 days. At the end of the paper, the type-I transfer is generalized (with some modifications) to the ephemeris model and some example transfer trajectories are given. Although only the transfer from $L_2$ to $L_4$ is studied in this paper, the same orbit design strategy can be generalized to the transfer to the triangular libration point $L_5$, and the transfers from the collinear libration point $L_1$ to triangular libration points.