  It is shown that the Baer-Kaplansky theorem can be extended to all abelian
groups provided that the rings of endomorphisms of groups are replaced by
trusses of endomorphisms of corresponding heaps. That is, every abelian group
is determined up to isomorphism by its endomorphism truss and every isomorphism
between two endomorphism trusses associated to some abelian groups $G$ and $H$
is induced by an isomorphism between $G$ and $H$ and an element from $H$. This
correspondence is then extended to all modules over a ring by considering heaps
of modules. It is proved that the truss of endomorphisms of a heap associated
to a module $M$ determines $M$ as a module over its endomorphism ring.
