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The LHCb collaboration presents a novel suite of heavy-flavour jet substructure measurements at forward rapidity in proton-proton collisions at a centre-of-mass energy of 13TeV. The jet mass is a perturbatively calculable probe of the virtuality of hard-scattered quarks and gluons, connecting small-distance quantum chromodynamics (QCD) with long-distance experimental measurement. The jet mass is dominated by nonperturbative corrections at small values, presenting an excellent test of QCD across a broad range of jet energies. Measuring heavy-flavour jet mass with a theoretically unambiguous flavour definition for the first time probes the gluon splitting mechanism for heavy-flavour production and offers tests of perturbative QCD at new levels of theoretical precision. Utilising the soft drop jet-grooming technique to access the perturbative jet core further enhances constraints on first-principles theory. Measurements of the jet mass for jets containing fully reconstructed hadrons are reported with and without grooming. The unique phase space instrumented by LHCb offers a different quark-gluon fraction than at midrapidity. These results offer unparalleled tests of quark flavour and mass dependence in QCD and provide a baseline for future studies of heavy-flavour jet quenching in heavy-ion collisions.