The instructions provided describe how to enable z-values on an existing shapefile to associate with vertices in ArcMap.
The instructions assume a field of z-values already exists in the attribute table of the shapefile.
In the Table Of Contents, right-click the shapefile, and open the attribute table.
In the Table Options, select Export, and click the folder button to browse for a location to save the table. Save the Output table in the dBase Table format (.dbf).
Add the Output table to the ArcMap document, and right-click the .dbf file in the Table Of Contents > Display XY Data.
In the Display XY Data dialog box, set the X, Y, and Z Field values, and click OK to create the event layer.
From the events layer, export the data to a new shapefile. Right-click the events layer > Data > Export Data, and determine the location for the shapefile.
Once the new shapefile is created, in the Table Of Contents, right-click the newly created shapefile, and select Properties > Source tab. Verify the coordinates have z-values enabled in the Data Source section.