According to Twitter, users can now pin their DM conversations for easier access.

Users may now pin up to six of their chats to the top of their DM inbox on Twitter. On iOS, pinned conversations were previously only available to Twitter Blue users. Users with the Twitter Blue subscription will still be able to upload longer videos.
Twitter has been improving its DM feature, starting with the ability to bulk-send Tweets without having to create a new account.
On iOS, users can access the option by swiping on an individual conversation, however on Android, users can just press and hold the message they want to preserve, and a “Pin Conversation” option should emerge.
The new functionality is currently accessible on iOS, Android, and the web.
Source: Twitter Support