  Superconductor-ferromagnetic heterostructures have been suggested as one of
the most promising alternatives of realizing odd-frequency superconductivity.
In this work we consider the limit of shrinking the ferromagnetic region to the
limit of a single impurity embedded in a conventional superconductor, which
gives raise to localized Yu-Shiba-Rusinov (YSR) bound states with energies
inside the superconducting gap. We demonstrate that all the sufficient
ingredients for generating odd-frequency pairing are present at the vicinity of
these impurities. We investigate the appearance of all possible pair amplitudes
in accordance with the Berezinskii $SP^{\ast}OT^{\ast} = -1$ rule, being the
symmetry under the exchange of spin, spatial, orbital (in our case $O=+1$) and
time index, respectively. We study the spatial and frequency dependence of of
the possible pairing amplitudes, analyzing their evolution with impurity
strength and identifying a reciprocity between different symmetries related
through impurity scattering. We show that the odd-frequency spin-triplet
pairing amplitude dominates at the critical impurity strength, where the YSR
states merge at the middle of the gap, while the even components cancel out
close to the impurity. We also show that the spin-polarized local density of
states exhibits the same spatial and frequency behavior as the odd-$\omega$
spin-triplet component at the critical impurity strength.
