This topic addresses this question:
How do you capture things that are not really stakeholder requirements, e.g. things like “the system shall auto-generate an 8 digit ID number”?
There is a couple of ways that you can deal with non-functional requirements, system constraints and other not so obviously “user centred” requirements such as this.
Depending on the scope of the requirement, you could write it as a story or in to the acceptance criteria.
Your particular example looks like it is at a level of detail that it could be written in to the acceptance criteria.
For example,
As a university student want to submit an online admissions application so that I receive an offer quickly.
Given that I am a registered applicant in the system, when I select the application, then the system displays a page with the following:
<<describe page elements, fields and buttons and other characteristics here.>>
Given that I have completed the form, when I submit the application, then the system:
<<describe all the things the system does, e.g. Display an application summary with all fields submitted and unique 8 digit number for my reference.>>
With other non-functional requirements, you can actually write them as a story as well.
For example, if the business wants the system to be available 99% of the time, you could write something like this:
As a user, I want the site to be available 99% of the time I try to access it, so that I don’t get frustrated and find another site to use.
Also, it is understandable that all requirements are not user facing – and that’s normal. I come across this all of the time. So your example also looks like a very good candidate for the feature driven development syntax (FDD).
The syntax for FFD is this: [action] the [result] [by|for|of|to] a(n) [object]
For example: Generate a unique 8 digit identifier for the application record.
I quite like the FDD approach as it deals with certain types of requirements that are a bit removed from the user, and the requirement doesn’t have to be forced in to the story format.
Even though I have given the option to write it in to the story, I favour FDD for this example.