How can I add this on my welcome screen
lets say a button that...
Add to favorites / Add to home
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I think the user must do this themselves in the browser. Browsers don't let you do it automatically to stop spammers filling up your home screen and favourites.
Not sure about desktop, but for mobile devices you can implement a version of the google bookmark bubble to pops up and prompts users to add the page to the homescreen of your mobile device