I have Google Maps in my Android App. I added it by selecting new Google Maps Activity & pasting the key in Android Studio. It worked fine in my Android phone (Lenovo K5
I think the SHA1 key you used to develop the app on pc is creating this problem on another pc. Generate SHA1 on new pc and replace old one then it will work fine.
As you are using it as debugging purposes. For production purposes there is documentation on developer page.