TOKYO, Dec. 21 -- Vodafone Group, a British telecommunications company, has agreed to buy a 15 percent stake in Japan's third-largest telecommunications company. Vodafone, the world's largest mobile phone service vendor, reached a final agreement Tuesday with two Japanese companies to buy 15 percent of the outstanding shares of Japan Telecom for $2.5 billion. Vodafone's investment will make it the second-largest shareholder in Japan Telecom, after East Japan Railway, which holds a 15.1 percent stake.