We are working on this feature right now! It should be available soon.

In the meantime, there is a way you can save text messages, if you want. Here’s how:

First, finish the conversation. Then, before you close the conversation tab, click the envelope icon at the top of the chat window. See it? Once you’ve converted the conversation into an email, you’ll notice it’s automatically addressed to the person you were texting with. If you want, go ahead and send it to them – a copy will also go into your Sent folder, where you can find it later.

You can also just delete their address from the “To:” field and put in your own! Then when you receive it, file it in whatever folder you want.