  The production of prompt $D^+_{s}$ and $D^+$ mesons is measured by the LHCb
experiment in proton-lead ($p\mathrm{Pb}$) collisions in both the forward
($1.5<y^*<4.0$) and backward ($-5.0<y^*<-2.5$) rapidity regions at a
nucleon-nucleon center-of-mass energy of $\sqrt {s_{\mathrm{NN}}}=8.16\,$TeV.
The nuclear modification factors of both $D^+_{s}$ and $D^+$ mesons are
determined as a function of transverse momentum, $p_{\mathrm{T}}$, and
rapidity. In addition, the $D^+_{s}$ to $D^+$ cross-section ratio is measured
as a function of the charged particle multiplicity in the event. An enhanced
$D^+_{s}$ to $D^+$ production in high-multiplicity events is observed for the
whole measured $p_{\mathrm{T}}$ range, in particular at low $p_{\mathrm{T}}$
and backward rapidity, where the significance exceeds six standard deviations.
This constitutes the first observation of strangeness enhancement in charm
quark hadronization in high-multiplicity $p\mathrm{Pb}$ collisions. The results
are also qualitatively consistent with the presence of quark coalescence as an
additional charm quark hadronization mechanism in high-multiplicity proton-lead
collisions.
