Context. A microlensed hyperspectral imager (MiHI) is an integral field spectrograph based on a double-sided microlens array.Aims. To convert the raw data frames of such an instrument to hyperspectral cubes, and restore them to high-resolution science-ready Stokes data, a new kind of data reduction procedure is required.Methods. An optimized ad hoc transfer map of a MiHI prototype was used to convert the raw data into raw hyperspectral form. The transfer map was modified to match the position of the image on the detector, which was found to drift considerably during the course of an observing day. The determination of this position was used to move the recorded flat-field images to the position of the observation, which was found to be a critical step in the accurate gain correction of the raw data cubes. The converted data were found to be suitable for image restoration but still contained unwanted polarimetric structure that needed to be removed.Results. The extracted and restored data were found to be of a similar spatial resolution as the equivalent data from the context imager, while retaining a spectral resolution of approximately 300 000. The noise properties of the raw data were determined by the photon statistics and were found to be consistent with the estimated transparency of the instrument and the integration time of the image sensor. As for all image-restored data, the noise properties of the restored data were found to be dependent on the instrumental and atmospheric point spread function. An attempt to compare the data to other similar data suggested that the data had a spectral and spatial information content comparable to that of a Hinode spectro-polarimetric scan, but with a higher spatial resolution and a temporal cadence of approximately 10s.