Clinical adoption of multi-shot diffusion-weighted magnetic resonance imaging (multi-shot DWI) for body-wide tumor diagnostics is limited by severe motion-induced phase artifacts from respiration, peristalsis, and so on, compounded by multi-organ, multi-slice, multi-direction and multi-b-value complexities. Here, we introduce a reconstruction framework, LoSP-Prompt, that overcomes these challenges through physics-informed modeling and synthetic-data-driven prompt learning. We model inter-shot phase variations as a high-order Locally Smooth Phase (LoSP), integrated into a low-rank Hankel matrix reconstruction. Crucially, the algorithm's rank parameter is automatically set via prompt learning trained exclusively on synthetic abdominal DWI data emulating physiological motion. Validated across 10,000+ clinical images (43 subjects, 4 scanner models, 5 centers), LoSP-Prompt: (1) Achieved twice the spatial resolution of clinical single-shot DWI, enhancing liver lesion conspicuity; (2) Generalized to seven diverse anatomical regions (liver, kidney, sacroiliac, pelvis, knee, spinal cord, brain) with a single model; (3) Outperformed state-of-the-art methods in image quality, artifact suppression, and noise reduction (11 radiologists' evaluations on a 5-point scale, $p<0.05$), achieving 4-5 points (excellent) on kidney DWI, 4 points (good to excellent) on liver, sacroiliac and spinal cord DWI, and 3-4 points (good) on knee and tumor brain. The approach eliminates navigator signals and realistic data supervision, providing an interpretable, robust solution for high-resolution multi-organ multi-shot DWI. Its scanner-agnostic performance signifies transformative potential for precision oncology.