Search in Private messages.
 

Is there such a mod, or function which can allow me to enable users of my forum to perform search within their private messages?

It's part of 3.8, no? Is that what you are talking about?

Search is allowed in private messages in 3.8? How?

On the bottom of the Private Message page - you can search for sender, title, and date range.

You can download them and search like that. That's the only way I know of. Unless Lynne has noticed something I haven't

You know, I only use that search for looking for PMs from certain users, so didn't see it doesn't actually do a search in the body.

You can look in the Add-Ons forums and search through just the Private Message Add-ons and see if they have what you want.