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 presence of spin-orbit coupling. Here we report devices in which triplet supercurrents are created and are injected into the s-wave superconductor Nb. In the normal state of Nb, triplet pairs decay over a distance of 5 nm, which is an order of magnitude smaller than the decay of zero spin singlet pairs due to the spin-orbit coupling interacting with the spin associated with a triplet supercurrent. In the superconducting state of Nb, triplet supercurrents are blocked by the lack of available equilibrium states in the singlet superconducting gap. The results offer new insight into the dynamics between s-wave singlet and triplet states.