turn off the ability of a user to delete an invoice

Is there a way that I can "Turn off" a user's ability to delete an invoice?  I am thinking that under user roles -- invoice data entry - uncheck the box for "remove". Does this sound correct?

We are having an issue with a user bringing sales orders into invoices, electronically delivering the invoices to the customers and then deleting the invoices. These invoices are not updated to the subledger and as such, do not appear on the customer's account. However, not all our customers reconcile thier monthly statements and will just pay each individual invoices. As such, there are some "prepayments" on invoices that do not exist in our system.  I am unable to track which user it is because there is no historical record of the deleted invoices (another feature that I would like to change...to be able to audit transactions (updated, deleted or otherwise))

Thank you.