Here is the situation. Admin has received the user claim through private conversation and reported it to make the original claim visible and discussionable for the rest of staff. Unfortunately in my case it's not visible for mods.
User group > Moderating > Personal Conversation Moderator Permissions, Edit post by anyone - Allow.
The same is set manually for every (super)moderator.
Btw is there any other way to make a userclaim public if received in conversation?