Don't understand the question. The modem would still have to be plugged in to the socket (or cable socket if using Virgin) - and if the modem is not a combined router the router would plug into the modem.
But telephone line suggests a dial up connection. He must be on broadband to go wireless.
If he is out and about with it then he will be able to connect to the internet using WIFI hotspots. Places such as Mc Donalds, Starbucks and loads of other places have them. When at home he'd still need to connect via his broadband router / modem to an ISP.
This site lists some of the hotsopts available in the UK
It is a hard question to understand. The simple answer is if he is at home and his laptop was wireless, there'd be no physical lead to the laptop. The only connection would be the router to your phone socket, for which, as said, you would have to have a working broadband supplier in place.