What is my religious duty towards my neighbors after I noticed suspicious actions by the wife and daughter in the husband's absence? Should I inform him, try to advise her, or remain silent?

The default assumption for a Muslim is blamelessness, and harboring ill thoughts about them without clear evidence is forbidden, as Allah Almighty says: ﴿O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin.﴾, and the Prophet, peace and blessings be upon him, said: «Beware of assumption, for assumption is the falsest of speech.» What has been rumored about the woman and her daughter are mere claims that do not necessitate accusation. Monitoring their home and investigating their affairs is impermissible, as it is a form of forbidden espionage. If their reprehensible conduct is proven, it is very serious and harms her reputation and her husband's reputation. Offering her advice is obligatory, for a woman is commanded to preserve her husband in his absence. If advice does not work, she can be threatened with informing her husband, or the husband can be alerted implicitly or explicitly to fulfill his duty. Divorcing a woman who does not repent is recommended to protect the family from corruption.