Comment 1 for bug 514426

Your contact likely set her presence to "invisible". To you it seems your contact is offline. Thus, you can assume a realtime chat conversation will not be possible. Hence, the only possibility is to send a normal message using an email style interface.

Allowing users to send chat messages to offline contacts does not seem to be a good idea to me. Some not so smart users would have difficulties understanding the concept of offline contacts. You might get annoying chat conversations to offline contacts like this:
15:00: Hi
15:02: How are you?
15:05: ????
15:07: Hello??!!
15:10: Why don't you answer me?

The email-like interface for messages of the type normal does not at all indicate there will be a realtime answer from the contact.

"I suggest to add a possibility to compose messages to the off-line contacts using a Chat window."

This is won't fix, but maybe you have another suggestion to improve the interface regarding this issue?

"This will also provide saving outgoing messages to off-line contacts into history, I believe (this bug has been reported before)."
Messages of the type normal should not appear in the conversation history. See: http://xmpp.org/rfcs/rfc3921.html#stanzas