With the new version of BBM you do have the option of storing your conversations to your memory card. However, if you do not already have this option selected then you are not able to recover your conversation.
And what do you mean by viewing the entire conversation? In the chat window you should be able to scroll up to the when the conversation started. If you're storing the chats in your memory card then you're also able to go back and view old chats in their entirety.
The latest version of Blackberry Messenger is 126.96.36.199. If you do not have the latest version you can download it from Blackberry App World or by going to www.blackberry.com/messenger from your Blackberry browser.