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The historical supernova SN 1181 remained unidentified for decades. In 2021, a strong candidate for its remnant was finally discovered, revealing several unique properties not seen in other supernova remnants (SNRs). Most notably, the SNR contains a white dward (WD) and the central WD is currently emitting a fast stellar wind at 15,000 km/s. This high-velocity wind is likely colliding with the ejecta of SN 1181, forming a termination shock. Consequently, the remnant exhibits a multi-layered X-ray structure: thermal X-ray emission is observed from both the shocked SNR and an inner emission region, as revealed by XMM-Newton. We analyzed Chandra X-ray data of this central emission and developed a theoretical model that reproduces the observed X-ray structure. Our analysis suggests that the fast wind from the WD began relatively recently, around 1990. To investigate this delayed wind onset, we performed WD evolution calculations using the stellar evolution code MESA, demonstrating that a delay of approximately 1,000 years is feasible. Furthermore, our calculations constrain the properties of the central WD, allowing us to constrain the progenitor system of SN 1181, which remains poorly understood.