Teodosiu joined the national team at the age of 18, after the 2012 Summer Olympics, when three of its four members retired from sport. His first competition with the team was the Madrid World Cup, where Romania earned a bronze medal. Mădălin Bucur was selected in his place for the 2013 European Fencing Championships in Zagreb, but head coach Mihai Covaliu called him back as reserve for the World Championships in Budapest. In the individual event, he was eliminated in the table of 64 by Valery Pryiemka of Belarus. In the team event, Romania defeated Australia, then Poland, and hosts Hungary to meet Belarus in the semi-final. Teodosiu entered the piste on 30-24 for Belarus and defeated Aliaksei Likhacheuski 11–4 to give his team the lead. Romania finally prevailed 45–44. In the final against Russia, Teodosiu lost 5–7 his first relay against Nikolay Kovalev, as well his second, with 4–6 against newly crowned World champion Veniamin Reshetnikov. Romania were defeated 45–38 and took the silver medal.