Include side-conversations in search function

We deal with several parties in our conversations. Often half a conversation is being held in a side-conversation. Currently side-conversations are not in any way searchable in Help Desk.
This means a huge portion of all our communication is lost in a non-searchable “black hole”.
The messages from a user in side-conversations don’t show up under Messages & Conversations under the user in contacts and it’s not possible to find it in any way except from manually scrolling and reading through hundreds/thousands of conversations to maybe find something that you can not even see if it will exist to begin with.
Basically, it very strongly inhibits the possibility to keep a clear track of past conversations.
I would very much like to see side-conversations included in search, since they are fully a part of the conversation as a whole. Users, titles and message content.