In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of \emph{resources}—a form of state transition systems—to describe the state-based program invariants that must be preserved, and to record the permissible atomic changes to program state. In this paper we introduce a novel notion of \emph{resource morphism}, i.e.~structure-preserving function on resources, and show how to effectively integrate it into separation logic, using an associated notion of morphism-specific \emph{simulation}. We apply morphisms and simulations to programs verified under one resource, to compositionally adapt them to operate under another resource, thus facilitating proof reuse.