You would need to google for the best solution for you setup if indeed you are using a local web server.
If you mean local network volume. Then normally no.
You can write to file by using something like this. ( picking up the text from the form first.
But that will go to the downloads folder.
There are ways that you can also talk to the system via apps/script/browsers but that is involved and a security risk.
It may be possible to use google Extension Options , I have used this for preferences for a Chrome Extension, which gets sync to the users account. But again involved and you probably would need to build an extension.
And this is only for Chrome
Your best bet is to have the user input stored on localStorage.