Mac Messages sending to Wrong Computer

I recently purchased a new mbp to replace an older one. However, I forgot to disable the imessages feature on the old mpb before giving it to a family member. That family member and I both discovered that the messages that should be going to the new mbp are going to the old mbp.

How do you get the messages that were on the old mbp onto the new mbp? I do not have access to the old mbp, and the family member logged out without thinking and could not simply read the messages to me.

Any ideas?