If it's business I'd obtain personal domain, yourname.com or whatever. You don't need to purchase or create website to utilize email services for it. Here is an example plan, it's not a recommendation. Pricing doesn't include domain registration so you can add about $10 to the annual cost.
https://www.namecheap.com/hosting/email/
Forward the att/bellsouth emails to either your new domain or the gmail account whichever you want to use. Look for any options about auto responder so emails sent to those accounts get auto reply with "Received your email but our new email address is (gmail account or domain)". If att/bellsouth control panel doesn't have this Outlook should.
Forward either the gmail account to the new domain or vice versa.
Last but not least you access Gmail or
you@you.com with outlook and since you are forwarding everything to that account all your email is there.
When he gives out email address use the
you@you.com because this can never be lost as long as you keep paying the domain registration.... You are at the mercy of any company when it's
you@somecompany.com If you stop doing business with them or they simply decide to stop service it's bye, bye email account.