just to add, telegram can NOT transfer or back up E2E encrypted chats either. unencrypted chats transfer because they are saved on the telegram server.

i think deltachat is possibly the only one that can transfer encrypted messages because you can copy the encryption keys and the messages are just mails, easy to copy (and usually stored on your mail server too)

i don't know how matrix handles this, but from the way verification works there, i am not confident.