Sequential Recommendation (SR) models infer user preferences from interaction histories. While transferable Multi-modal SR models outperform traditional ID-based approaches, existing methods struggle with slow fine-tuning convergence due to complex optimization requirements and negative transfer effects. We propose MMM4Rec (Multi-Modal Mamba for Sequential Recommendation), a novel Multi-modal SR framework that incorporates a dedicated algebraic constraint mechanism for efficient transfer learning. By combining State Space Duality (SSD)'s temporal decay properties with a globally-aware temporal modeling design, our model dynamically prioritizes key modality information, overcoming limitations of Transformer-based approaches. The framework implements a constrained two-stage process: (1) sequence-level cross-modal alignment via shared projection matrices, followed by (2) temporal fusion using our newly designed Cross-SSD module and dual-channel Fourier adaptive filtering. This architecture maintains semantic consistency while suppressing noise propagation. By incorporating algebraic structural constraints aligned with SR priors, MMM4Rec employs a simple and consistent cross-entropy objective across both pre-training and fine-tuning, enabling rapid fine-tuning convergence, substantially improving multimodal recommendation accuracy, and preserving strong transferability. Extensive experiments demonstrate MMM4Rec's state-of-the-art performance, achieving strong multi-modal retrieval capability and exhibiting 10$\times$ faster average convergence speed when transferring to large-scale downstream datasets. The implementation is available at link https://github.com/AlwaysFHao/MMM4Rec.

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