If the "Show previous messages to new members" setting is enabled in the conversation, then the conversation history is disclosed to new members automatically. If the setting is disabled, then there are 3 different ways how you can disclose previous messages to new members.
Option 1: Open the members tab, click on the member that has been added to the conversation and choose Disclose history from the drop-down menu that appears. Now, all of the conversation history is available to the user you chose.
Note that if you click on someone who already has access to the message history then you will not see the option Disclose history in the drop-down menu.
Option 2: You can also choose to disclose message history starting from a specific point/message in the conversation. For that you need choose the message, launch the message actions menu and choose Disclose history. This will open up a new window, where you can choose the member(s) to whom you wish to disclose the message history.
Option 3: Disclose conversation when adding a new member into the conversation. In the Add members popup, there is a checkbox that says "Disclose previous messages to new members". If you enable this, the new members will be able to see conversation history.
IMPORTANT! Do note that these actions can't be taken back. Once you've disclosed conversation history to someone, they will see the history until they delete the conversation.