Actually the image you are looking at is not from any browser like Safari or Chrome.
It is generated by the Router you are tying to connect to.
That is why the browsers wont help you if you try to use saved passwords.
However, once connected and on the Internet, if you loose that connection for some reason then the browser will help you reconnecting and automatically supply the saved password. So save it in Browser and on you key cahin.
You question is how to automatically provide a login to the Routers pop up login window.
There is a problem.
Since that pop up is not associated with any programs on you computer they can not do the auto-fill.
But there is a very simple solution.
Do as usual, when connecting.
Now the surprise: IGNORE the pop up window!!
Yes you can close that popup window.
Go to your browser where you have saved the login and call that website from your bookmarks.
In your case it should have this
Surprise, now the browser will login and fill out the password for you.