Transmission spectroscopy has been a workhorse technique used over the past two decades to constrain the physical and chemical properties of exoplanet atmospheres1–5. One of its classical key assumptions is that the portion of the atmosphere it probes—the terminator region—is homogeneous. Several works from the past decade, however, have put this into question for highly irradiated, hot (Teq ≳ 1,000 K) gas giant exoplanets, both empirically6–10 and through three-dimensional modelling11–17. While models have predicted clear differences between the evening (day-to-night) and morning (night-to-day) terminators, direct morning and evening transmission spectra in a wide wavelength range have not been reported for an exoplanet so far. Under the assumption of precise and accurate orbital parameters for the exoplanet WASP-39 b, here we report the detection of inhomogeneous terminators on WASP-39 b, which has allowed us to retrieve its morning and evening transmission spectra in the near-infrared (2–5 μm) using the James Webb Space Telescope. We have observed larger transit depths in the evening, which are, on average, 405 ± 88 ppm larger than the morning ones, and also have qualitatively larger features than the morning spectrum. The spectra are best explained by models in which the evening terminator is hotter than the morning terminator by 177‑57+65 K, with both terminators having C/O ratios consistent with solar. General circulation models predict temperature differences broadly consistent with the above value and point towards a cloudy morning terminator and a clearer evening terminator.