Installed PWA link vs open in new browser

If you have a PWA installed and running with service worker is there any way to txt or email a link and have that link open in the installed PWA instead of a new browser on mobile?

I realize that the PWA is just running in a browser but when it is installed it does not show the address bar and I need every bit of screen space.

If someone already has the PWA installed and running and they receive a link I would like it to open in the installed version versus opening another browser and having it run twice.
Is this a possibility?

Obviously this is not a problem on desktop. Only mobile.

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could you solve this?