The recently computed ExoMol line lists for isotopologues of AlH are used to analyse the blue spectrum (4000-4500 Å) of Proxima Cen (M5.5 V). Comparison of the observed and computed spectra enables the identification of a large number of 27AlH lines of the A 1Π -X 1Σ+ band system: The spectral range covering 1-0, 0-0, and 1-1 bands are dominated by clearly resolved AlH lines. We reveal the diffuse nature of transitions close to the dissociation limit which appears in the form of increasingly wider (up to 5 Å) and shallower (up to the continuum confusion limit) AlH line profiles. The predicted wavelengths of AlH diffuse lines are systematically displaced. The effect of broadening by predissociation states on the line profiles is included by increasing the radiative damping rate by up to 5 orders of magnitude. We determine empirical values of damping rates for a number of the clean 0-0 Q-branch transitions by comparing the observed and synthetic stellar spectra. We find excellent agreement between our damping rates and lifetimes available in the literature. A comparison of 27Al1H ExoMol and REALH spectra shows that the observed spectrum is better described by the ExoMol line list. A search for 26Al1H lines in the Proxima Cen spectrum does not reveal any notable features; giving an upper limit of 27Al1H /26Al1H >100.