ثُمَّ أَتِمُّوا الصِّيَامَ إِلَى اللَّيْلِ
Then complete the fast until the night.
The permissibility of intimacy continues through the night. A person may therefore reach dawn while still in a state requiring ghusl. The fast begins with dawn, while the bath can be performed afterward.
The text’s temporal arrangement implies that entering dawn in that state does not, by itself, invalidate the fast. This is ishārat al-naṣṣ, since that legal issue is not the principal topic of the permission.
The conclusion concerns fasting only. It does not remove the separate purification requirement for performing prayer.