On 26th September 2022, NASA's Double Asteroid Redirection Test (DART) mission actively impacted the small moon Dimorphos of the Didymos-Dimorphos binary asteroid system. The impact caused a variation of about 33 minutes in its orbital period around Didymos and demonstrated the feasibility of moving an asteroid in space. As part of an international observing campaign devoted to its physical characterization, in this work we investigate the visible spectral properties of the Didymos-Dimorphos system soon after the impact. Rotationally-resolved spectra have been obtained 25 days after the impact and two months later. Geometric investigations have been performed to look for the source region corresponding to each spectrum. Here we show an overall agreement with pre-impact spectra and S-type classification despite subtle variations emerging, possibly correlated with mutual events. Furthermore a small long term color evolution from October to December spectra tentatively interpreted as related to dust cloud grain size effects or alternatively attributed to an uneven deposition of freshly exposed material from the impact on Didymos.