I wrote here already that it’s common for what business considers a business process to become several process pools in BPMN - look at process patterns “internal order” or “incoming processor”. In both examples the “client” process posts a task into DB and process to wait message from the “server” process that the task is completed.
The diagrams are valid but here is the caveat: server should know the client internals - namely the event on the client side. It’s ok if the server deals with a single client but what if not?