It was later revealed that he was in fact not Kyouko's half-brother. Kyouko's family had adopted him, meaning they were not related by blood.
After the Road to Symphonia in Pretty Rhythm: Dear My Future, Jun proposed to Kyouko at Rizumu & Hibiki's wedding, saying "Please marry me." Although shocked, she later accepted, and wearing the engagement ring he gave her, they headed to his parents' grave for him to introduce her to them, and report that he was getting married to her.
