If this string is stored in an object you might want to associate it with entity Session and set the association on create with $currentSession. Then after sign-in you can retrieve the object from $currentSession on your page.
Can you provide a bit more context? Where will this “district” value be coming from? Are you expecting this to come from an external system somewhere? Are you using SSO?
As an example, you can usually pass through SAML Assertion Attributes containing this type of information if you use the SAML module. You can then link this value to your user/account through the “CustomUserProvisioning” microflow. These assertion attributes are controlled by your Identity Provider. Below is a link to how someone set up SSO with Okta. Look specifically for the “assertion data” section in this blog post:
How to use the SAML module with IDP Okta
Or use a deeplink where you pass this parameter. If a user needs to login first it will show the signin page. But then it will continue with the deeplink so that you have an the user and the parameter to do the stuff you want.