...to make them work with mobile in browsers iOS, Android, or windows phone.
Aren't they already working in mobile browsers?
And how would Phonegap be a factor in your project?
Yes, it works but the UI is not proper as the controls are meant for desktop browsers (e.g. big gridviews). i mean having two sets of pages each with proper UI and controls that fit for best OS, Browser, and screen size.
I was reading some articles about cardova to convert your normal web sites or web applications to mobile adaptable web sites. I was thinking that PhoneGap might have same option, assuming PhoneGap was driven by cordova.
In that case I feel that you are misinterpreting the role of Phonegap/Cordova.
However, the UI would still be yours, where you would style your UI with CSS using techniques called 'responsive' or 'liquid' layouts. Phonegap will not force or support your liquid UI development.
Again: the UI (liquid/responsive) is created by you and fed to Phonegap. Phonegap (be it locally installed or with the Phonegap Build cloud service) will then turn your assets into a hybrid installable app.
Now, if you are looking for a web app which is executed/displayed in the mobile browser (and not in an app's webview component), then Phonegap will not come into play for your purposes. You would simply focus on creating a liquidly designed UI.