The Workflow Management Coalition, WfMC for short, has given a protocol for interorganizational workflows, interworkflows for short. In the protocol, an interworkflow is constructed by connecting two or more existing workflows; and there are three models to connect those workflows: chained, nested, and parallelsynchronized. Business continuity requires the interworkflow to preserve the behavior of the existing workflows. This requirement is called behavioral inheritance, which has three variations: protocol inheritance, projection inheritance, and life-cycle inheritance. Van der Aalst et al. have proposed workflow nets, WF-nets for short, and have shown that the behavioral inheritance problem is decidable but intractable. In this paper, we first show that all WF-nets of the chained model satisfy life-cycle inheritance, and all WF-nets of the nested model satisfy projection inheritance. Next we show that soundness is a necessary condition of projection inheritance for an acyclic extended free choice WF-net of the parallelsynchronized model. Then we prove that the necessary condition can be verified in polynomial time. Finally we show that the necessary condition is a sufficient condition if the WF-net is obtained by connecting state machine WF-nets.