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[KoryKramer]

These only contain the .shp.  For ArcGIS to read these, your colleague will need to include all of the associated files.  See Shapefile file extensions—ArcMap | Documentation 

Depending on what all is in the folder with the shapefiles, it might be easiest for them to just zip the whole folder and send that.  Otherwise, find the filenames that correspond with the .shp files that they sent, and make sure they're include all of the files that have the same name with different extensions.

Quick example: