  In this work we derive the junction conditions for the matching between two
spacetimes at a separation hypersurface in the perfect-fluid version of
$f\left(R,T\right)$ gravity, not only in the usual geometrical representation
but also in a dynamically equivalent scalar-tensor representation. We start
with the general case in which a thin-shell separates the two spacetimes at the
separation hypersurface, for which the general junction conditions are deduced,
and the particular case for smooth matching is considered when the
stress-energy tensor of the thin-shell vanishes. The set of junction conditions
is similar to the one previously obtained for $f\left(R\right)$ gravity but
features also constraints in the continuity of the trace of the stress-energy
tensor $T_{ab}$ and its partial derivatives, which force the thin-shell to
satisfy the equation of state of radiation $\sigma=2p_t$. As a consequence, a
necessary and sufficient condition for spherically symmetric thin-shells to
satisfy all the energy conditions is the positivity of its energy density
$\sigma$. For specific forms of the function $f\left(R,T\right)$, the
continuity of $R$ and $T$ ceases to be mandatory but a gravitational
double-layer arises at the separation hypersurface. The Martinez thin-shell
system and a thin-shell surrounding a central black-hole are provided as
examples of application.
