We have used the Atacama Pathfinder Experiment 12 m telescope (APEX) to carry out an absorption study of submillimeter wavelength rotational ground-state lines of H35Cl, H37Cl, 13CH+, and, for the first time, of the SH+ radical (sulfoniumylidene or sulfanylium). We detected the quartet of ground-state hyperfine structure lines of SH+ near 683 GHz with the CHAMP+ array receiver against the strong continuum source Sagittarius B2, which is located close to the center of our Galaxy. In addition to absorption from various kinematic components of Galactic center gas, we also see absorption at the radial velocities belonging to intervening spiral arms. This demonstrates that SH+ is a ubiquitous component of the diffuse interstellar medium. We do not find clear evidence for other SH+ lines we searched for, which is partially due to blending with lines from other molecules. In addition to SH+, we observed absorption from H35Cl, H37Cl, and 13CH+. The observed submillimeter absorption is compared in detail with absorption in 3 mm transitions of H13CO+ and c-C3H2 and the CO J = 1-0 and 3-2 transitions.This contribution is dedicated to the memory of John M. Brown, pioneer of submillimeter spectroscopy of free radicals.