In this paper, we address the problem of task-informed grasping in scenarios where only incomplete or partial object information is available. Existing methods, which either focus on task-aware grasping or grasping under partiality, typically require extensive data and long training durations. In contrast, we propose a one-shot task-informed methodology that enables the transfer of grasps computed for a stored object model in the database to another object of the same category that is partially perceived. Our method leverages the reconstructed shapes from Gaussian Process Implicit Surfaces (GPIS) and employs the Functional Maps (FM) framework to transfer task specific grasping functions. By defining task functions on the objects' manifolds and incorporating an uncertainty metric from GPIS, our approach provides a robust solution for part-specific and task-oriented grasping. Validated through simulations and real-world experiments with a 7-axis collaborative robotic arm, our methodology demonstrates a success rate exceeding 90% in achieving task-informed grasps on a variety of objects.