  We present a variant of a universality result of R\"odl [On universality of
graphs with uniformly distributed edges, Discrete Math. 59 (1986), no. 1-2,
125-134] for sparse, $3$-uniform hypergraphs contained in strongly jumbled
hypergraphs. One of the ingredients of our proof is a counting lemma for fixed
hypergraphs in sparse ``pseudorandom'' uniform hypergraphs, which is proved in
the companion paper [Counting results for sparse pseudorandom hypergraphs I].
