In this paper we address the problem of migrating instances between heterogeneous overlapping ontologies. The instance migration problem arises when one wants to reclassify a set of instances of a source ontology into a semantically related target ontology. Our approach exploits mappings between ontologies, which are used to reconcile both conceptual and individual level heterogeneity, and further used to draw the migration process. We ground the approach on a distributed description logic (DDL), in which ontologies are formally encoded as DL knowledge bases and mappings as bridge rules and individual correspondences. From the theoretical side, we study the task of reasoning with instance data in DDL composed of SHIQ ontologies and define a correct and complete distributed tableaux inference procedure. From the practical side, we upgrade the DRAGO DDL reasoner for dealing with instances and further show how it can be used to drive the migration of instances between heterogeneous ontol...