The accurate measurement of the solar spectrum at the top of the atmosphere and its variability are fundamental inputs for solar physics (Sun modeling), terrestrial atmospheric photochemistry, and Earth's climate (climate's modeling). These inputs were the prime objective set in 1996 for the SOLAR International Space Station (ISS). The SOLAR package represents a set of three solar instruments measuring the total and spectral absolute irradiance from 16 nm to 3088 nm. SOLAR was launched with the European Columbus space laboratory in February 2008 aboard the NASA Space Shuttle Atlantis. SOLAR on the ISS tracked the Sun until it was decommissioned in February 2017. The SOLar SPECtrum (SOLSPEC) instrument of the SOLAR payload allowed the measurement of solar spectra in the 165{\thinspace}--{\thinspace}3000 nm wavelength range for almost a decade. Until the end of its mission, SOLAR/SOLSPEC was pushed to its limits to test how it was affected by space environmental effects (external thermal factors) and to better calibrate the space-based spectrometer. To that end, a new solar reference spectrum (SOLAR-ISS -- V1.1) representative of the 2008 solar minimum was obtained from the measurements made by the SOLAR/SOLSPEC instrument and its calibrations. The main purpose of this article is to improve the SOLAR-ISS reference spectrum (between 165 and 180 nm in the far ultraviolet, between 216.9 and 226.8 nm in the middle ultraviolet, and between 2400 and 3000 nm in the near-infrared). SOLAR-ISS has a resolution better than 0.1 nm between 165 and 1000 nm, and 1 nm in the 1000{\thinspace}--{\thinspace}3000 nm wavelength range. Finally, a first comparison is made between the new SOLAR-ISS spectrum (V2.0) and the Total and Spectral solar Irradiance Sensor (TSIS-1) spectrum obtained from its first observations from the ISS. Indeed, the launch of TSIS in December 2017 provides a new light on the absolute determination of the solar spectrum and especially in the infrared region of the spectrum.