Recording or logging conversations is not difficult. I've included instructions below: 

• Open the "Edit" menu in Second Life (at the top) and choose "Preferences"
• Click the Communications tab and check the boxes shown with red checkmarks under "Logging Options"
• To more easily locate your transcripts later, change the "path" to something that will be easy to remember (it'll point you to whatever folder you want to save your chats in - and you can create a folder specifically for this purpose).