If you want to save your chat on facebook, you can use add-ons firefox Facebook Chat History Manager. This add-ons allow you to save your Facebook chat messages in your local environment. After Facebook Chat History Manager installed (restart firefox require), from Firefox menubar, select Tools, find Facebook Chat History Manager menu, and select Create Account.
The ID used to create local account is a ten or more digit number that facebook used to identify each member. An account is necessary to ensure one can only view his/her own messages. The chat history manager will save your chat message automatically and silencely. To Get Facebook ID, From Tools->Facebook Chat History Manager, select "Get Facebook ID", then login to facebook to get your facebook ID. This add-ons work with Firefox 1.5 - 4.0b8pre.