The shortcut icon is created automatically when you install an application from Google Play (based on Google Play settings). It is never created automatically in other cases.
Some how, shortcut icons were appearing on the screen of my test phone. Now they are not, so it is a curiosity to me.
My more important question is if there is a way for me to give the app to individuals to test prior to making it available on Google Play. I intend to pursue this either way, but I would like to do some controlled testing first.
The icon is added to your list of apps when the app is installed, however, if you don't see the icon being added to your HOME screen that means the setting to do so in the Google Play app has changed (Add Icon To Home Screen).
My more important question is if there is a way for me to give the app to individuals to test prior to making it available on Google Play. I intend to pursue this either way, but I would like to do some controlled testing first.
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