An inhomogeneous magnetic exchange field at a superconductor/ferromagnet interface converts spin-singlet Cooper pairs to a spin-aligned (i.e. spin-polarized) triplet state. Although the decay envelope of such triplet pairs within ferromagnetic materials is well studied, little is known about their decay in non-magnetic metals and superconductors, and in particular in the presence of spin-orbit coupling (SOC). Here we investigate devices in which triplet supercurrents are injected into the s-wave superconductor Nb. In the normal state of Nb, triplet supercurrents decay over a distance of 5 nm, which is an order of magnitude smaller than the decay of spin singlet pairs due to the SOC interacting with the spin associated with triplet pairs. In the superconducting state of Nb, triplet supercurrents are not able to couple with the singlet wavefunction and thus blocked by the absence of available equilibrium states in the singlet gap. The results offer new insight into the dynamics between s-wave singlet and s-wave triplet states.