Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If your wife prays Fajr before the sun rises, even if it is only few minutes before sunrise, then she has prayed on time, and she is not sinful.
Answering your question, The Fatwa Center at Islamweb, states:
The time of Fajr begins from the beginning of the true dawn and extends until sunrise.
If your wife prays Fajr before the sun rises, even if it is only few minutes before sunrise, then she has prayed on time, and she is not sinful. She only misses the reward of praying at the beginning time.
Delaying the prayer close to its ending time constantly is believed to lead to negligence and, eventually, delaying it until its time expires.
Some jurists are of the view that it is disliked to delay the Fajr until the morning light starts to spread (this happens shortly before sunrise). Rather, some jurists are even of the view that it is forbidden to do so.
However, if she prays after the time of the prayer expires [i.e. after sunrise], then she is not praying on time; rather, she is praying outside its fixed time and she is sinful for the delay if she is negligent.
An example for this is if she wakes up when you wake her up but she does not stand to pray and delays it until its time expires.
Another example is if she delays the prayer (after waking up) too close to sunrise in a way that she prays part of the prayer after its fixed time; in which case, she is sinful and the threat of neglecting the prayer applies to her. We read in the Quran:
“So woe to those who pray. [But] who are heedless of their prayer.” (Al-Ma`un 107:4-5)
“But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil.” (Maryam 19:59)
It is obligatory on her to fear Allah Almighty and offer the prayer on its prescribed fixed time. She should be keen on performing the prayer at the beginning of the fixed time, because this is greater in reward for her and protects her from laziness and from delaying the prayer until its time ends.
There is a Hadith warning those who come late and do not pray in the first row, although this is only desirable. The Hadith reads: “Some people will continue to be late (i.e., miss praying in the first row) until Allah will put them at the back (rows).” (Muslim)
How would the case be for the one who delays performing the prayer that Allah has imposed upon him/her until its time expires? One must be careful about this.
Almighty Allah knows best.
Source: http://www.islamweb.net/en/fatwa/385633/she-prays-fajr-15-minutes-before-sunrise