  The form factors of the descendant operators in the massive Lee-Yang model
are determined up to level 7. This is first done by exploiting the conserved
quantities of the integrable theory to generate the solutions for the
descendants starting from the lowest non-trivial solutions in each operator
family. We then show that the operator space generated in this way, which is
isomorphic to the conformal one, coincides, level by level, with that implied
by the $S$-matrix through the form factor bootstrap. The solutions we determine
satisfy asymptotic conditions carrying the information about the level that we
conjecture to hold for all the operators of the model.
