  We study the correspondence theory of intuitionistic modal logic in modal
Fairtlough-Mendler semantics (modal FM semantics) \cite{FaMe97}, which is the
intuitionistic modal version of possibility semantics \cite{Ho16}. We identify
the fragment of inductive formulas \cite{GorankoV06} in this language and give
the algorithm $\mathsf{ALBA}$ \cite{CoPa12} in this semantic setting. There are
two major features in the paper: one is that in the expanded modal language,
the nominal variables, which are interpreted as atoms in perfect Boolean
algebras, complete join-prime elements in perfect distributive lattices and
complete join-irreducible elements in perfect lattices, are interpreted as the
refined regular open closures of singletons in the present setting, similar to
the possibility semantics for classical normal modal logic \cite{Zh21d}; the
other feature is that we do not use conominals or diamond, which restricts the
fragment of inductive formulas significantly. We prove the soundness of the
$\mathsf{ALBA}$ with respect to modal FM frames and show that the
$\mathsf{ALBA}$ succeeds on inductive formulas, similar to existing settings
like \cite{CoPa12,Zh21d,Zh22a}.
