Storing player passwords locally

Maybe I wasn’t clear enough;

I have a server setup with registration and login on an external website as well as a login in the UE4 game. Passwords are hashed and salted when registered. Used a Rest plugin to fully integrate with UE4, players can login and create sessions by sending JSON requests.

What I need is to be able to have a remember password button so the player doesn’t have to type in their password every time. Similar to how a Firefox or Chrome browser can remember passwords or like Star Citizen. How would a browser or game store the passwords on the users local pc?