You could try temporarily setting the Group to allow the Public to post by email moderated -
and then set the incoming Feedburner email to always post in the group.
But doing that would allow anyone else to post to the group using a different Feedburner feed.
A much better option is to subscribe to the Feedburner feed by email
with an address that is a member of the group and setup a filter
in that email to forward those emails to the group.
If using gmail , use periods in the address you use for subscribing to the feed
to make the filtering easier.
There are other options, outside of Feedburner , for sending immediate emails
to the group when a new post is published on the blog - not once a day at your
chosen schedule like in Feedburner.