By default you can use the "h" key to show a bit of extended chat-history on-screen; gives just enough time to read the messages in, i.e. say a very busy cruise server.
But I don't think what you're asking is available. Unless the insim application in your server logs the PMs you get and makes them accesible elsewhere. You can save replay and check chat (tedious task) but even that won't save/show insim messaged (PMs sent via the insim).
There might be something; make sure to check back.