When using Gmail chat from different devices, like a browser, a phone and a tablet, it doesn't matter from which of these devices you write your messages, they are going to be replicated in every device.
For example, if from my browser where gmail is opened, I say something to someone, I will see that thing replicated in the phone and in the tablet.
This way, you can follow the full conversation (both what I say and what the other person say), in any of the devices I want to use.

If I'm using telepathy to chat with someone, if I stop writing in telepathy and move to some other device, like my phone, and continue chatting with this person, I will see these messages in my browser and tablet, but not on telepathy.

If I have a full conversation with someone, I will see the full conversation in every device, but in telepathy, I will only see messages from the other person.

Would it be possible for telepathy to replicate this functionality?

Reproducible: Always

Steps to Reproduce:
1. Open Google Talk in several devices (Browser, phone, tablet) and in telepathy
2. Start a conversation with someone using telepathy
3. All your messages appear in every other device
4. Switch to any of the other devices and start writing
Actual Results:  
None of your messages appear in telepathy. Only the replies from the person you're talking with

Expected Results:  
You get your messages, even if you didn't wrote them in telepathy. The conversation looks the same in any of the devices and in telepathy