Had a quick look in PDM standard and I don't seem to see any options like what you are looking for. PDM Pro seems to be the same thing if you are using the PDM notifications and sending system. Could be a different story if you instead use the emailing systems available with PDM Pro.
Even in PDM Pro, the system does not keep track of 'sent' notifications. It clears that SQL table after send to save space, which in most cases, is ideal.
If using SMTP (in Pro), you could just check the email server.
I like the idea of sending the user a copy of the notification as well. A user can hold a notification in their inbox as long as they want, even when the notifications table is cleared. Per your specific scenario, I would test that first.
There is an enhancement request for this that I would encourage you to vote on: SPR 588110 - Inbox should have a 'Sent Items' to store notifications that are manualy sent to other users (Notify a colleague...)