Decomposing edge-coloured complete symmetric digraphs into monochromatic paths

Confirming and extending a conjecture by Guggiari, we show that every countable $(r+1)$-edge-coloured complete symmetric digraph containing no directed paths of edge-length ${\mathrm{\ell }}_i$ for any colour $i\le r$ can be covered by ${\prod }_{i\le r}{\mathrm{\ell }}_i$ pairwise disjoint monochromatic directed paths in colour $r+1$.