Is it permissible for the husband to specify a time for intercourse, either before or after Fajr, so that his wife can perform Fajr prayer and avoid laziness due to ritual impurity (janabah), and what is the ruling on the wife delaying Fajr prayer until sunrise on non-school days despite being reminded of it?

There is no harm in linking intercourse to the time of Fajr with the intention of helping the wife perform the prayer, while observing the wife's right to enjoyment.

The husband bears a great responsibility in encouraging his wife towards good, and prayer is the greatest pillar of Islam after the two Shahadas.

The husband must alert his wife and wake her for prayer, and exert efforts to that end, such as explaining the ruling on neglecting prayer and encouraging her to perform it.

It is recommended to wake the wife for prayer by sprinkling water on her face if she refuses to wake up, as narrated from the Prophet, peace and blessings be upon him.

The wife should be encouraged to sleep early, warned against staying up late, advised gently and kindly, and encouraged and rewarded for praying.

If the wife continues to be negligent, it is permissible to resort to strictness sometimes, such as shunning her, to achieve benefit and reform her, while being patient with her and not becoming exasperated.