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The production of prompt Λc+ baryons at midrapidity (|y|<0.5) was measured in central (0–10%) and mid-central (30–50%) Pb–Pb collisions at the center-of-mass energy per nucleon–nucleon pair √sNN=5.02 TeV with the ALICE detector. The results are more precise, more differential in centrality, and reach much lower transverse momentum (pT=1 GeV/c) with respect to previous measurements performed by the ALICE, STAR, and CMS Collaborations in nucleus–nucleus collisions, allowing for an extrapolation down to pT=0. The pT-differential Λc+/D0 ratio is enhanced with respect to the pp measurement for 4<pT<8 GeV/c by 3.7 standard deviations (σ), while the pT-integrated ratios are compatible within 1σ. The observed trend is similar to that observed in the strange sector for the Λ/KS0 ratio. Model calculations including coalescence or statistical hadronization for charm-hadron formation are compared with the data.