No add-on is needed to do this, vBulletin has this feature built-in, the admin that has access to the Forum & Moderators section of the ACP only needs to add a prefix to every forum or those where "Solved" is needed and then optionally add an HTML markup to it to make it stand out in the thread listing (red color, italic, bold etc.).
However, if there is a time limit for users to edit their own posts, then only moderators and the admin himself will be able to add the "Solved" prefix after that time has passed, so in order for users to be able to do it themselves, they should be allowed to edit their posts indefinitely. Of course, most admins tend to avoid that option being enabled, I don't know how is it here, I just registered.
It's a really simple vB feature and can turn out to be very useful for tech support forums which is why most of them use prefixes anyway, not just the "Solved" one, but multiple prefixes and prefix sets depending on the forum and the type of thread for easier navigation and much better overview, as well as searching - you are, for instance, given the option to only search for "Solved" threads. In the long run, this can even take some load off the system resources (which particularly goes for tech support forums often taking hits from members and visitors alike searching the board for answers, thus making constant queries across the entire server) especially if after a while the admin decides to add something like a subforum to every forum called "Known problems solved" or something in that vicinity.
Anyway, great idea to have this forum, everyone, as a fresh
N95 user, this comes in very helpful. Thanks a lot.