Unlike e-mail, PMs stay in the Outbox until the recipient opens them. Then they are transferred to the Sent Box. Nothing you can do to speed up how long it takes someone to notice it's there, I'm afraid!
This is also complicated by browsers that block pop-ups; anyone who has not deactivated their pop-up-blocker for this web site is apt to miss PMs because they will not get a notification window to alert the user to the messages' arrival. And, considering the number of PMs that have been in my Outbox for several weeks, not everyone notices the count at the top of each page where it says either, "You have no new messages" or "You have X
Hope this helps.