Open installed PWA from external url
If you are using Chrome in Android or any of the desktop OS, that would be the default behavior.
Check on "Android intent filter" in this link.
This feature is not supported in iOS yet for PWA apps(created using Safari- the only option for iOS as of June-2018).See "What PWAs can do on Android and not on iOS" section last point.
For iOS, there is actually a very unknown way which you can install a .mobileconfig profile which installs a web clip (or multiple web clips if you like).
This will run your website in fullscreen and is very similar to how iOS PWAs work. You can also link to it online or send it as an Email attachment for your users to install.
Just make sure you add this for the webpage to open fullscreen:
<key>FullScreen</key>
<true/>
You can read more about creating your own from scratch here:
https://developer.apple.com/library/archive/documentation/NetworkingInternet/Conceptual/iPhoneOTAConfiguration/ConfigurationProfileExamples/ConfigurationProfileExamples.html
or if you have a Mac you can get the "Apple Configurator 2" App:
https://apps.apple.com/us/app/apple-configurator-2/id1037126344
or you can take the easy route and use a generator here if you don't have a Mac:
https://webclip.glitch.me/