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 (ﷺ) is His Slave and Messenger.
It is not Islamically obligatory for a husband to inform his wife of the details of his personal affairs, just as it is not obligatory for a wife to inform her husband of the details of her personal matters. Likewise, it is not permissible for a husband to search through his wife’s phone, as this falls under spying, which is prohibited in Islam. The prohibition of spying is established in both the Qur’an and the Sunnah.
Both spouses must fear Allah regarding one another and should live together in kindness and according to what is reasonable. Each spouse is also required to fulfill the rights of the other. Allah, The Exalted, says (what means): {And due to the wives is similar to what is expected of them, according to what is reasonable.} [Quran 2:228]
Part of living together in a good and reasonable manner is that when either spouse sees the other falling into something wrong, they should offer sincere advice with wisdom, gentleness, and kind speech. They should also regularly supplicate for one another, asking Allah to grant them righteousness and goodness.
Allah Knows best.