Basemap not showing up when saving Shapefile

I am very much a beginner here.

I am trying to create a Shapefile to send to an agency to indicate where I will be conducting field work. I am using OCM Landscape Basemap, and I just have a few points added as Shapefile layers to indicate where my field sites are. However, when I save and try to open the Shapefile, there is no Basemap, and all I see are my little dots. How do I save a map with my field sites (as my little dots) and the Basemap in the Shapefile format?