Snapshot Broadband Filter Array (BFA) imaging provides high light throughput for spectral reconstruction but introduces severe spectral aliasing due to complex modulation. Current deep learning approaches, limited to spatial denoising, often fail to address the global frequency-specific degradations caused by the mask structure. To address this, we propose a Physics-embedded Frequency-aware Transformer (PF-Trans) for high-fidelity remote sensing spectral reconstruction. Our method explicitly integrates the physical sensing model through mask injection and a gray-scale consistency loss to ensure physical fidelity. Furthermore, we introduce a Dual-domain Block with a parallel Fast Fourier Transform (FFT) branch, enabling the network to perceive and suppress aliasing artifacts in the frequency domain. Extensive experiments on multiple datasets demonstrate that PF-Trans achieves state-of-the-art performance, achieving a Peak Signal-to-Noise Ratio (PSNR) of up to 48.50 dB on the GF-5 Shanghai dataset, significantly outperforming comparison methods.