What is the ruling on a husband talking with young men and women who work in prostitution networks via Messenger, with the intention of exposing these networks, and is it permissible for the wife to feel jealous about that?

Conversation via Messenger is permissible as long as it does not include anything prohibited by Sharia. What the husband does by spying and lying is originally impermissible, but if it becomes a necessary means to uncover corruption, then there is no harm in it due to an overriding benefit. If the husband shows a negative impact from this action, he must be advised to stop it. The wife's jealousy is natural, but one must beware of blameworthy jealousy that is not based on a sound foundation.