Observations of the frequencies of different rotational transitions of the methanol molecule have provided the most sensitive probe to date for changes in the proton-to-electron mass ratio, μ, over space and time. Using methanol absorption detected in the gravitational lens system PKSB1830−211, changes in μ over the last 7.5 billion years have been constrained to |Δμ/μ| ≲ 1.110 −7 . Molecular absorption systems at cosmological distances present the best opportunity for constraining or measuring changes in the fundamental constants of physics over time; however, we are now at the stage where potential differences in the morphology of the absorbing systems and the background source, combined with their temporal evolution, provide the major source of uncertainty in some systems. Here, we present the first milliarcsecond resolution observations of the molecular absorption system towards PKSB1830−211. We have imaged the absorption from the 12.2-GHz transition of methanol (which is redshifted to 6.45GHz) towards the southwestern component and show that it is possibly offset from the peak of the continuum emission and partially resolved on milliarcsecond scales. Future observations of other methanol transitions with similar angular resolution offer the best prospects for reducing systematic errors in investigations of possible changes in the proton-to-electron mass ratio on cosmological scales.