The ability to search your Conversations (AKA Private Messages/PMs) is being made available to Supporting Members and Vendors at this time. This is a 3rd party add-on by a US developer that I've know for a few years. I feel it is well supported, stable, and secure. Conversation search is one of the most requested feature for the core forum software and I believe at some point in the future it will be included in the default installation.