The 0-Hecke algebra is a generalization of Symmn whose representations behave similarly to the representations of Symmn. In particular, there is a nice correspondence between projective representations of Hn(0) and compositions of n, which also index ribbon Young diagrams, skew Young diagrams that do not contain any 2×2 box. We study branching rules for projective indecomposable representations of Hn(0). In particular, we show a branching rule for these representations at the level of characters in NSym, and then exhibit an explicit short exact sequence that these representations satisfy.