I don't believe it is possible to do it automatically because messages recorded using Live Record are sent directly to the mailbox of the person that conferenced it in.

However you could create a general mailbox specifically for this purpose and instruct the users to forward any Live Record messages to the new mailbox. If you have IMAP licenses you could set up an IMAP connection for a specific user for this new Live Record general mailbox and save the attachments manually to wherever you wanted them.

It's not the prettiest solution, and you would be relying on the users to forward the messages but it should work.