The interconnection of weak electric power grids opens new issues into power system stability and control. This paper proposes a control strategy of HVDC transmission yielding increased power transfer capacity and enhanced transient stability of weak interconnected systems. The proposed control is a recently developed synchronverter-based control and emulation of the HVDC link (SHVDC). Methodologically, the transient stability of the neighbouring zone is a priori taken into account at the design level of the control. The parameters of the SHVDC regulators are tuned based on a specific residues method. The performances of the control strategy are analyzed by the power transfer limit Plimit when the interconnection is a pure DC link, and by both the Plimit and the Critical Clearing Time (CCT) when the interconnection is a hybrid DC/AC link. The study further investigates the impact of the inertia emulation that the synchronverter provides, and of the tuned control parameters on Plimit. The proposed control is tested in comparison to the standard vector control. The simulation results indicate that the synchronverter based control improves both the dynamic transfer capacity and the transient stability of weak interconnected power systems.