When you want to say that someone is no longer doing what they were doing before, use the pattern stop doing something, not ‘stop to do something’:
✗ People have practically stopped to write letters to each other.
✓ People have practically stopped writing letters to each other.
The pattern stop to do something means that someone stops what they are doing in order to do something else. It tells you the reason why someone has stopped.
He stopped to light a cigarette.
(= he stopped talking, walking, working etc, in order to light a cigarette)
He has stopped smoking.
(=he used to smoke, but he doesn’t smoke now)