Is delaying Fajr prayer until after the Adhan, with the strong presumption of oversleeping and missing its time, considered intentional negligence, and does it necessitate uttering the Two Testimonies, and is it permissible to delay making up missed prayers in this manner?

A Muslim should hasten to obey Allah and avoid obeying Satan and the soul that incites evil (nafs al-ammarah bi al-soo'), which calls for laziness in prayer, especially the 'Isha and Fajr prayers, which are considered the heaviest prayers for hypocrites. The questioner should not succumb to Satan's deception by beautifying sleep until she misses the Fajr prayer at its early prescribed time. If she sleeps after the time for prayer has begun, knowing or thinking that she will not wake up before the time expires, she must repent from intentionally delaying the prayer without a legitimate excuse. She does not need to re-perform the prayers she prayed after waking up, and this is not considered apostasy. If she misses prayers whose time has expired and has not made them up, she must make them up immediately. If she cannot determine their number, she should make up what she believes is the probable number. Whoever performs one rak'ah of a prayer before its time expires has caught the prayer in performance, as the Prophet, peace and blessings be upon him, said: "Whoever catches a rak'ah of Fajr before the sun rises has caught it, and whoever catches a rak'ah of 'Asr before the sun sets has caught it."