Out of the box the System Administrator has permissions to be able update the Unit Price of an Invoice Product on an a Paid Invoice. 
Is this a permission that is available in Security Roles, or is it a back end system thing for users with the System Administrator security role?
I've tried using the Override Invoice Pricing permission but it doesn't work. Below is a screenshot of the Sales permissions for the security role in question, it has pretty much everything, but when the user tries to update the Unit Price of a paid Invoice Product they get an error message saying "The product cannot be saved because the parent cannot be edited.". The log file for this error message is also attached.


[View:/cfs-file/__key/communityserver-discussions-components-files/762/ErrorDetails-_2D00_-2020_2D00_05_2D00_12T082237.395.txt]