Is it permissible to pray behind the elder brother who misses some prayers and listens to music, or does the younger brother have the right to step forward and lead the prayer?

The obligatory prayers should be performed in the mosque in congregation, and one must answer the call of the muezzin if the mosque is near. The more preponderant opinion is that prayer behind a transgressor (fasiq) is valid. This is supported by the general statement of the Prophet, peace and blessings be upon him: "The people are led in prayer by the one among them who is most knowledgeable of the Book of Allah...", and by the Companions' prayer behind Al-Hajjaj, and by the principle that whoever's prayer is valid, his imamate is also valid. It is preferable for you to lead the prayer instead of your brother if you meet the conditions for preferential imamate mentioned in the hadith (definition) and you are upright. The Permanent Committee gives precedence in leading prayer to someone with a beard, even if he has memorized little (of the Quran), over someone who shaves his beard, even if he has memorized the entire Quran.