What one needs to do is to “Share” the device that has already joined the Echo Matter/Thread to HA. I have not done this myself, but other users report that you go to the Alexa App, and choose the Matter device you want to share, and there you should find some option to share it with other assistants (or something like that) and it should provide you with a sharing code. Then you go to HA and add the device as a Matter device.