Archer's next post after COS Starfleet is in '69 as Ambassador to Andoria, if Christopher keeps to Sussman's timeline.
That idea never made much sense to me. Even allowing for the idea that the UFP's Members would have "ambassadors" to the UFP like the U.N.'s Member States -- which is redundant, because the UFP is a sovereign state (unlike the U.N.) and its Members already have Federation Councillors -- the idea that the UFP would have an ambassador to its Members is... weird. The U.N. does not have ambassadors to its Member States -- its Member States have ambassadors to
it.
Could he be the Earth ambassador to Andoria? We know that Federation worlds have embassies to one another. (Right? You pay much more attention to this stuff than me.)
Federation Member States do maintain diplomatic missions to one-another (Sarek was established in ST09 to be the Vulcan Ambassador to United Earth, for instance), so, yeah, I think your idea that he becomes United Earth Ambassador to the Andorian Empire makes a bit more sense than Federation Ambassador to the Andorian Empire. And, indeed, I just checked, and
the bio screen seen in "In A Mirror, Darkly" does not specify
whose ambassador to Andoria he was, so there's wriggle room for your interpretation there!
The idea of Federation Member States maintaining diplomatic missions to one-another is a little odd by modern standards, since it's not as though the
Länder of Germany or
states of India exchange ambassadors between each-other. But it does make sense that the Federation, even if it is a sovereign federal state, would function differently than a real-life federal state -- it is, after all, larger than any sovereign state that has ever existed in real history, even from its onset. So it makes sense that Federation law would allow its Member States to practice direct bilateral relations with one-another as a matter of practical necessity, presumably subject to Federation review. And there is some real-world precedent for this -- states in the U.S. can enter into
interstate compacts with one-another with the consent of the U.S. Congress. Some interstate compacts can even accept foreign polities -- the Province of Ontario and the Province of Québec are both associate members of the
Great Lakes Commission.
I have the feeling that the title "ambassador" has a different meaning in the Federation than it has today, perhaps due to alien influence.
An alternate possibility is that sometimes, the term "ambassador" may be used informally but inaccurately. For instance, you often hear of Ambassadors to the U.N. -- but their actual title by law is
Permanent Representative to the United Nations. Maybe the representative of one Federation Member State to another has a different title by law, but is referred to as "ambassador" informally.
