Screen defined attributes do not save to the user store and cannot be retrived and used in other locations such as in an email body.
This is by design as screen defined attributes only exist in the scope of the visual screen. The documentation implies this by saying that they are defined locally for the current task. The Screen logical attribute can be used to modify data in the userstore to display on the screen only but not actually do any true modifications to the data itself.
You need to create an LAH that properly maps data to an underlying userstore. In the User Console, task screen fields are associated with data attributes. Logical and Physical attributes. Physical attributes are attributes of the underlying data store. If a task screen field is configured with a physical attribute, a value entered into the field is ultimately written to the data store. Logical attribute values are not directly associated with or written to the data store. A logical attribute value is presented in a task screen field and processed by a logical attribute handler.
These two attribute definitions are needed in order to have an attribute on a task screen saved for future saving/manipulation. The documentation below shows how to configure these properly.