Frame your case, step by step.

1. In Safari, tap Share : the square with the upward arrow.
2. Scroll down the list and tap Add to Home Screen .
3. Tap Add at the top right: the firm’s icon appears with your other apps.

Apple does not allow websites to install themselves: the three steps have to be done by hand, and only once. This works in Safari: if the page is open inside another app, open it again in Safari.