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Messages sent from the Messages Beta desktop app show up on your iDevice, too. New messages are appended to existing conversations.
On iOS devices, new messages exchanged with users in existing conversations appear in the old thread. This means you can take all of your conversations with you no matter what Apple computing device--Mac or iOS device--you're using.
One odd thing: On my daughter's iPhone, the new conversation we had showed up separately from existing conversations. I'm not entirely certain why. We had previously traded text messages and iMessages in a single conversation. After I installed and started using Messages Beta, the conversation I started on my Mac showed up in a separate thread on her iPhone.