This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
A Convertor is not a good place to do this, for several practical reasons, but the abstract reason why you shouldn't do it there is that a Convertor should not be altering data.
What I would generally do would be something like this. I'd lay out a page with the inputs, including country selection and phone number, with a separate control for the country code part of the phone number. Depending on your preferences/needs, this control might be display-only. You could then attach AJAX functionality so that whenever the country selection control value was changed, a backing bean action method (AJAX listener) computed the corresponding country code and set the backing bean property for the country code accordingly.
A variation on this where you don't maintain a separate control for the country code is to make the AJAX listener code strip any detected previous country code from the input phone number and replace it with the new country code.
An IDE is no substitute for an Intelligent Developer.