All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
The sin of deliberately neglecting prayer until its time has passed is borne by the wife, not the husband, because it is she who neglected the prayer, not the husband. Allah says: {And every soul earns not [blame] except against itself, and no bearer of burdens will bear the burden of another.} [Quran 6:164] However, the husband may be considered sinful if he fails to offer necessary advice to his wife or does not prevent her from neglecting her prayers out of laziness. This responsibility falls under the duty of enjoining good and forbidding evil, and neglecting this duty, when it becomes obligatory, is a sin.
Concerning the husband’s responsibility for not waking up his wife for prayer, then this depends on the guidelines regarding waking up a sleeper. If it is recommended to wake someone for prayer, then the husband is not sinful for not doing so. However, if it is obligatory, then failing to wake her up would be a sin. In Al-Majmu’, Imam An-Nawawi states: “Waking a sleeper for prayer is recommended, especially if the time is about to end, as evidenced by the verse stating: {And cooperate in righteousness and piety} [Quran 5:2] and the Hadith in which ‘Aa'ishah reports: ‘The Messenger of Allah, sallallaahu 'alayhi wa sallam, used to offer prayer at night while I was sleeping across in front of him; and when the Witr prayer was yet to be observed, he would wake me up and I would pray Witr prayer.” [End quote]
Some scholars view that waking someone up for obligatory prayers could indeed be mandatory. Thus, in Al-Mufhim, Al-Qurtubi remarks: “It could be said that this act is obligatory in case of obligatory prayer, for whereas the sleeper is not accountable while asleep, his impediment can be easily removed, like someone who is merely heedless. It is undoubtedly obligatory to alert the heedless.” [End quote]
Thus, it is prudent for the husband to make efforts to wake up his wife for prayer. If he knows she tends to be neglectful and lazy about her prayers, he should promptly advise her and remind her of Allah, in the hope that she will heed his advice, become mindful, and consistently perform her prayers.
Allah knows best.