Ok, so the email failing is the one being sent to the admin to notify the admin a birthday email was sent, correct?
The From address does not have a setting (in Connections or this addon). The address is pulled from the email address entered on the WP General Settings admin page.
If the address shown in the log does not match the email address found on the WP General Settings admin page then there must be another plugin installed which is overriding the address in that setting.
Does that help?