Personal message after exiting the conversation can not be returned back to the user. When prompted, the user back to the correspondence, nothing happens.

Hello @Ilya Kirilenko this has been the case since 3.x series. When a user leaves the conversation it is then deleted and they cannot be reinvited to it. A new conversation would need to be started to include this member.

It is not an option because many participants in the conference, and a lot of messages. And there are a lot of conferences. Some users mistakenly go out and get them back into the same conference can not?

There is no way to get someone back into a private conversation after they leave.