Under both Add client and Edit client, you can select the country under Mobile, Home, and Work.  Just click on the flag (defaulted to the US) and select the country from the dropdown list.

That's purely for your internal records only.  If your client is to sign up for or already has an Intuit account, he/she will enter a phone number for Intuit records (e.g. for MFA).  What you enter/change your client's phone numbers in ProConnect Tax, that will not affect your client's Intuit account in any way.