Sciex, you might be interested in a few features that are already supported by the forum. They're similar to what you're asking about, and some (particularly the 2nd and 4th) might directly address your needs. I've listed them below:
First, PMs can be quoted much like posts can. If you click "Quote" rather than "Reply" when viewing a PM in your inbox, you'll be presented with a form to send a reply PM with a quote of the recipient's previous message already filled in. This can help to provide contexts for individual messages, though the act of doing this helps your
recipient, not you (unless your recipient does this as well).
PMs can also be sorted by varying criteria, including by sender or by subject. Just click the corresponding header on the list of PMs to change their sorting order. At that point, you can browse through the pages of PMs in search of the username or subject line you're looking for. This might address part of what you were looking for in your opening post.
In addition, the forum's PM inbox supports labeling. See the
Manage Labels link on the left sidebar of the PM bar. Once a label's created, it can be applied to inbox messages by selecting the corresponding checkboxes by the message entries and then selecting the appropriate entry from the "Label Selected:" dropdown underneath those checkboxes. Messages associated with a given label can be viewed by clicking the label's name on the left sidebar of the PM screen; this makes labels useful for being able to have quick, repeated access to a category of related PMs. Note, though, that messages in your
outbox cannot be given a label.
Last but not least, PMs support
searches and even
advanced searches, just as the main forums do. See (once again) the left sidebar for these features. Advanced searches are powerful; you can search by label, by author, and by either title or content of the PM. However, you'll only be able to find messages in your inbox this way; your outbox won't be searched. Regardless, this may address another part of what you requested in your opening post, since you can still filter out PMs sent by a specific member as part of the search criterion in this fashion (without the need to create and maintain labels to do so).
I hope the info dump was helpful and informative. If you find that the features I've listed don't address all of your concerns, don't be afraid to clarify or to give more details relevant to the user experience you're looking for.
GrayWolf, I'm not aware of a way to present a conversation view of forum PMs (aside from the use of quoting). Having said that, if you haven't already, you might find
the Furtopia IRC server to be of interest. You can have text based chats with other online users (either through PM, through one of the public chatrooms, or through creating your own room on the server), and if you use an IRC client (rather than the web client I just linked), you can take advantage of its logging function to save a record of the conversation on your own computer.