Motor imagery electroencephalography (MI-EEG) decoding offers a non-invasive route for post-stroke rehabilitation, but cross-patient use remains difficult because pathological neural reorganization changes task-related EEG dynamics, aperiodic activity, local excitability, cross-regional coordination, and trial-level brain-state context. This makes source-learned MI representations unreliable for unseen patients. To address this problem, we propose CFSPMNet, a cross-patient adaptation framework that models post-stroke MI-EEG as latent neural-state organization. CFSPMNet combines a Fourier-Reorganized State Mamba Network (FRSM) with Shared-Private Prototype Matching (SPPM). FRSM represents each trial as a latent physiological token sequence, reorganizes token states in the Fourier domain, and uses Fourier-derived trial context to guide Mamba state-space propagation. SPPM improves target pseudo-label updating by combining semantic confidence with shared-private physiological consistency, filtering confident but physiologically inconsistent target predictions. Leave-one-subject-out experiments on two stroke MI-EEG datasets show that CFSPMNet outperforms representative CNN-, Transformer-, Mamba-, and adaptation-based baselines, achieving average accuracies of 68.23% on XW-Stroke and 73.33% on 2019-Stroke, with gains of 5.63 and 8.25 percentage points over the strongest competitors. Ablation, sensitivity, feature-alignment, pseudo-label selection, and neurophysiological visualization analyses further support the roles of Fourier-domain token-state reorganization and calibrated pseudo-label updating. These results suggest that latent neural-state modeling can improve rehabilitation-oriented cross-patient BCI decoding. Code is available at https://github.com/wxk1224/CFSPMNet.