Is it obligatory to inform the mother about the sexual conversations that the questioner previously discovered, or is it sufficient to conceal them after learning of her repentance, and is the absence of conversations with men sufficient to judge her repentance?

Inspecting the mother's mobile phone is not permissible except in certain circumstances, and it is a prohibited form of spying. As long as the mother has repented and no suspicion has arisen from her, do not inform her of the evil you discovered, conceal her faults, think well of her, and pray to Allah to keep her away from what is forbidden. You are not a cuckold (dayouth), for a dayouth is one who approves of immorality among his family. The mother's right is great and is not negated by falling into sins, so strive to honor her and treat her kindly.