In 2015, Torne et al. reported detections of the magnetar SGR J1745-2900 up to 225 GHz (1.33 mm), which was the highest radio frequency detection of pulsar emission at that time. In this work, we present the results of new observations of the same magnetar with detections up to 291 GHz (1.03 mm), together with evidence of linear polarization in its millimetre emission. SGR J1745-2900 continues to show variability and is, on average, a factor ~4 brighter in the millimetre band than in our observations of 2014 July. The new measured spectrum is slightly inverted, with 〈α〉 = +0.4 ± 0.2 (for Sν ∝ να). However, the spectrum does not seem to be well described by a single power law, which might be due to the intrinsic variability of the source, or perhaps a turn-up somewhere between 8.35 and 87 GHz. These results may help us to improve our still incomplete model of pulsar emission and, in addition, they further support the search for and study of pulsars located at the Galactic Centre using millimetre wavelengths.