What is the ruling on a husband searching his wife's phone without reason, given that there is trust between them and no fundamental problems, knowing that he found a personal conversation of hers complaining about him to her sister during a moment of distress?

It is not permissible for a husband to inspect his wife's phone or read her messages without her permission, because that is a form of spying which is prohibited by the Almighty's saying: "And do not spy." Spying is forbidden except in cases of extreme suspicion to prevent an evil or ward off harm. The marital relationship should be based on understanding, affection, and compassion.