If both apps are on the same box / have access to the same database (e.g. distributed servers), then this is as easy as setting a flag in the database and making sure both apps look for this flag and auto-login as needed.
Otherwise, the first thing that comes to mind is to have a special key generated for the user that’s send between apps to warn said app of an incoming already-logged-in user. This will of course be more complicated in terms of determining a proper “identity token” generation algorithm and keeping the transaction secure.
You can’t share sessions or cookies across sites.