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Core-collapse supernova remnants are structures of the interstellar medium (ISM) left behind the explosive death of most massive stars ( ?40 M-?). Since they result in the expansion of the supernova shock wave into the gaseous environment shaped by the star's wind history, their morphology constitutes an insight into the past evolution of their progenitor star. Particularly, fast-mo ving massiv e stars can produce asymmetric core-collapse superno va remnants. We inv estigate the mixing of materials in core-collapse supernova remnants generated by a moving massive 35 M-? star, in a magnetized ISM. Stellar rotation and the wind magnetic field are time-dependently included into the models which follow the entire evolution of the stellar surroundings from the zero-age main-sequence to 80 kyr after the supernova explosion. It is found that very little main-sequence material is present in remnants from moving stars, that the Wolf-Rayet wind mixes very efficiently within the 10 kyr after the explosion, while the red supergiant material is still unmixed by 30 per cent within 50 kyr after the supernova. Our results indicate that the faster the stellar motion, the more complex the internal organization of the supernova remnant and the more ef fecti ve the mixing of ejecta therein. In contrast, the mixing of stellar wind material is only weakly affected by progenitor motion, if at all.