Can we save chat history on yahoo mail?

No, use "save to e-mail" feature instead

Can you save chat history in yahoo mail?
http://wiki.answers.com/Q/Can_you_save_chat_history_in_yahoo_mail

Can you save chat history in yahoo mail not on messenger?
http://wiki.answers.com/Q/Can_you_save_chat_history_in_yahoo_mail_not_on_messenger

Related
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Yahoo Web Messenger conversation/chat history
1. In the left navigation column, click Messenger.- The "Messenger" column appears.
2. At the top of the "Messenger" column, select your status (Available, Busy) | Conversation History.
Note: Conversation history can't be viewed from the Yahoo Mail mobile app.

Search chat history with certain person:
Just type "someone@yahoo.com" at input box and hit "Search Mail"