This paper examines the stability of a weak island namely Sumbawa-Lombok of Indonesian grid, interconnected with two infeed HVDC links facilitating 2 x 120 MW power transfer from Sumba and Flores Island. Through power flow, short circuit, small signal stability, resonance stability, and transient stability analyses, it is demonstrated that the existing infrastructure fails to support such transfer due to voltage drops, overloading, and stability limitations. Upgrading to 150 kV and its subsequent component resolves the small-signal and transient stability constraint as its grid strength is increasing. The current findings underscore that the primary limitation lies in the grid's infrastructure, not in dynamic or control constraints. The current result establishes the need for strategic grid reinforcements to support HVDC integration in weak systems and sets the stage for future research on optimizing the extent of such reinforcements.