The goal of multispectral and hyperspectral image fusion (MHIF) is to generate high-quality images that simultaneously possess rich spectral information and fine spatial details. However, due to the inherent trade-off between spectral and spatial information and the limited availability of observations, this task is fundamentally ill-posed. Previous studies have not effectively addressed the ill-posed nature caused by data misalignment. To tackle this challenge, we propose a fusion framework named PIF-Net, which explicitly incorporates ill-posed priors to effectively fuse multispectral images and hyperspectral images. To balance global spectral modeling with computational efficiency, we design a method based on an invertible Mamba architecture that maintains information consistency during feature transformation and reconstruction, ensuring stable gradient flow and process reversibility. Furthermore, we introduce a novel fusion module called the Fusion-Aware Low-Rank Adaptation module, which dynamically calibrates spectral and spatial features while keeping the model lightweight. Extensive experiments on multiple benchmark datasets demonstrate that PIF-Net achieves significantly better image restoration performance than current state-of-the-art methods while maintaining model efficiency.