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The production yield and angular anisotropy of prompt D+s mesons were measured as a function of transverse momentum (pT) in Pb-Pb collisions at a centre-of-mass energy per nucleon pair sNN−−−−√=5.02 TeV collected with the ALICE detector at the LHC. D+s mesons and their charge conjugates were reconstructed at midrapidity (|y|<0.5) from their hadronic decay channel D+s→ϕπ+, with ϕ→K−K+, in the pT intervals 2<pT<50 GeV/c and 2<pT<36 GeV/c for the 0-10% and 30-50% centrality intervals. For pT>10 GeV/c, the measured D+s-meson nuclear modification factor RAA is consistent with the one of non-strange D mesons within uncertainties, while at lower pT a hint for a D+s-meson RAA larger than that of non-strange D mesons is seen. The enhanced production of D+s relative to non-strange D mesons is also studied by comparing the pT-dependent D+s/D0 production yield ratios in Pb-Pb and in pp collisions. The ratio measured in Pb-Pb collisions is found to be on average higher than that in pp collisions in the interval 2<pT<8 GeV/c with a significance of 2.3σ and 2.4σ for the 0-10% and 30-50% centrality intervals. The azimuthal anisotropy coefficient v2 of prompt D+s mesons was measured in Pb-Pb collisions in the 30-50% centrality interval and is found to be compatible with that of non-strange D mesons. The main features of the measured RAA, D+s/D0 ratio, and v2 as a function of pT are described by theoretical calculations of charm-quark transport in a hydrodynamically expanding quark-gluon plasma including hadronisation via charm-quark recombination with light quarks from the medium. The pT-integrated production yield of D+s mesons is compatible with the prediction of the statistical hadronisation model.