  An invertible polynomial is a quasihomogeneous polynomial with the number of
monomials coinciding with the number of variables and such that the weights of
the variables and the quasi-degree are well defined. In the framework of the
search for mirror symmetric orbifold Landau-Ginzburg models, P.~Berglund and
M.~Henningson considered a pair $(f,G)$ consisting of an invertible polynomial
$f$ and an abelian group $G$ of its symmetries together with a dual pair
$(\widetilde{f}, \widetilde{G})$. We consider the so-called orbifold E-function
of such a pair $(f,G)$ which is a generating function for the exponents of the
monodromy action on an orbifold version of the mixed Hodge structure on the
Milnor fibre of $f$. We prove that the orbifold E-functions of
Berglund-Henningson dual pairs coincide up to a sign depending on the number of
variables. The proof is based on a relation between monomials (say, elements of
a monomial basis of the Milnor algebra of an invertible polynomial) and
elements of the whole symmetry group of the dual polynomial.
