  We study the influence of the electron-magnon interaction on the particle
transport in strongly disordered systems. The analysis is based on results
obtained for a single hole in the one-dimensional t-J model. Unless there
exists a mechanism that localizes spin excitations, the charge carrier remains
delocalized even for a very strong disorder and shows subdiffusive motion up to
the longest accessible times. However, upon inspection of the propagation times
between neighboring sites as well as a careful finite-size scaling we
conjecture that the anomalous subdiffusive transport may be transient and
should eventually evolve into a normal diffusive motion.
