You can view a full transcript of an SMS/text message conversation by doing the following:
Find the contact you want to view the conversation for.
Click on the 'View SMS Text Messages' button, (if you do not see this button, then no SMS conversation exists for the contact).
Click on Manage Contact.
From the drop down select 'Print Transcript'
Now you should have the option to Print, Save as PDF, etc. (options may vary by computer or device).