Please post your zimbra version, or better yet, add it to your forum profile.
(Starting from root account...)
Code:
su zimbra
zmcontrol -v
Also the version of the ZCO used by the secretary.
It sounds like she has an old version of ZCO. You may also have an old version of ZCS. Some old versions of Zimbra require a server-side setting to allow a user to send on behalf of another.
While an upgrade might be advisable, in the meantime just look in the admin GUI, locate the secretary's account, and look at Preferences. From there you can either give her the right to send as anyone, or the right to send as specific other users.
However there's one wrinkle, which is that if the the secretary is using a boss email address that isn't published in the GAL, she's not allowed to send mail on behalf of that address. This is true even for recent versions of ZCO/ZCS.
See
Bug 40031 - Back out prevention of "Send on Behalf Of" without server pref and
Bug 40032 - Need "Send on behalf of" pref for details.