Can't get the original message's objectId using REST but if you are looking for the details of the messages in the chain, that can be fetched.

Do a GET /vmrest/message/<messageobjectid>?details=true
on the message for which you want to get the details.
It will give you the detailed output in which there will be attachment information. Look for the attachments having content-type "message/rfc822". Those are the messages which were forwarded in this chain. There are all the details for those messages but not the objectid.
-Utkarsh