Praise be to Allah.
He may recite out loud, and there is nothing wrong with that, so that he should make it up as Allah prescribed it. When the Prophet (blessings and Allah be upon him) missed Fajr prayer and did not offer it until after the sun had risen, he prayed it as he used to pray it at the beginning of the day, after dawn had broken. In other words, one should pray it as it is prescribed, with two rak‘ahs in which recitation is done out loud. He should also offer the regular Sunnah prayer that comes before it, as the Prophet (blessings of Allah be upon him) did.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him).
Fatawa Nur ‘ala ad-Darb (2/735).