Not sure why this is in the Linux/FreeBSD section, but probably one of the easiest ways to go about this would be to just give your son the money for the bill this month. Put it into his bank account or something, and trust him to do the right thing with the money.
Otherwise you can call the Verizon Wireless customer support number: (800) 922-0204 and if you are able to provide some key details like the last four numbers of your son's SSN, then they should allow you to pay the bill over the phone.
Do note however, that Verizon and Verizon Wireless are two separate companies. Verizon is the result of several baby bells on the eastern seaboard merging. Verizon Wireless is a cellular phone carrier that is a joint venture with Vodaphone, a major European cellular carrier. Make sure you know which one you need to contact, because despite the name, there is something of a firewall between the two companies and Verizon CSRs won't be able to help you pay a Verizon Wireless bill and the other way around.