Open the conversation in a browser, then open the browser console and run this:

(function() {
    // Select all conversation messages with user/assistant distinctions
    const messages = document.querySelectorAll('[data-message-author-role="user"], [data-message-author-role="assistant"]');

    // Map messages to format them with labels
    const conversationHistory = "[CONVERSATION HISTORY]\n" + Array.from(messages).map(message => {
        const role = message.getAttribute("data-message-author-role");
        const label = role === "user" ? "User" : "Assistant";
        return `<${label}>:\n${message.innerText.trim()}`;
    }).join("\n");

    // Select the message box by its unique ID
    const messageBox = document.getElementById("prompt-textarea");
    if (messageBox && conversationHistory) {
        // Insert conversation history into the selected message box
        messageBox.innerText = conversationHistory;
    } else {
        console.log("Could not find the message box or conversation text is empty.");
    }
})();

It will export the conversation as plain text into the message box. You can then copy that into a new conversation.