It doesn't quite work like that. The messages that are sent in the DM or group chat are decrypted on the client that has access to the group. Once the message is decrypted the client throws away the decryption key (for forward secrecy). But keeps a separately encrypted log of the chat. This is what happens with Signal, Whatsapp, etc. Each device keeps a copy of the transcript but at no point are they trying to rebuild the conversation from past messages (because they no longer have the cryptographic state to do that). Make sense? It's definitely a trade off with this sort of approach; security for convenience in using lots of devices or different clients.