There is no working export today. The full assistant page at uni.xyz/unify does carry an Export chat button offering JSON, Markdown and Plain Text, and none of the three currently produces a file: the request fails and you are shown "Failed to export chat session". The reliable way to keep a conversation is to select the text in the chat and copy it.
Copying is the whole workaround
Scroll to the part you want, select it with the mouse, and copy. The transcript is ordinary text on the page, so it pastes into a document, an email or a note with its paragraphs and lists intact. Copy as you go rather than at the end: a long chat is awkward to select in one sweep, and the piece you actually need is usually one reply rather than the whole thread.
A chat has its own web address, and that is the better bookmark
Open a conversation and the address bar carries it, in the form uni.xyz/unify/session/ followed by the chat's identifier. Bookmark that and you land back in the same conversation, on any device you are signed in on. It is not a copy, so it lasts only as long as the chat does, but for "I want to get back to this" it beats a file.
Copy anything you need before you delete a chat
Deleting is not reversible and there is no way to read a deleted conversation back. If a chat holds a deadline the assistant confirmed, or text it drafted for you, take the copy first. See Deleting a chat.
Two things are not stored inside the chat anyway
- Images the assistant generated. They live in your render history, so they survive the conversation.
- Files you attached. An upload is stored against your account rather than against the chat.
So an export would not have been the only copy of either.
If you need a conversation on the record
The messages themselves are stored, and the UNI team can read them. If you need a conversation retrieved, quoted or removed, ask rather than hunting for a download. See How to reach human support.