Sorry to say it it, but I think that the Home Office was correct to give you IAS's phone number. I have a sinking feeling that the reason HO couldn't advise what category of extension your other half needs is that there isn't one.
Even if we could somehow rerun things so that the COA was issued earlier, and you had just got back from the registry office having registered your civil partnership, your other half would
still be needing to return to Brazil in order to apply for a visa...
The only difference would be that he would be applying as your civil partner, rather than as your
proposed civil partner, which is what he needs to do now. But the basic requirements as to support, accommodation, genuineness of the relationship, are the same, whether he's a civil partner or a proposed civil partner. The requirements are
here, on the UKVisas website.
I don't know whether you have followed the saga of the COA but, basically, when they were introduced, it was intended that they would only be issued for people who were in the UK for a medium to long term stay - the applicant had to have been admitted for more than six months (which ruled out visitors), and had to have more than three months left on their visa. I think this meant that, in many cases, applicants would be able to "switch" visa categories following their wedding or civil partnership registration, or, if this was not possible, at least they would be able to live together as man and wife or as registered partners for a decent length of time before leaving the country to make a spouse or civil partner visa application.
The COA regulations were challenged in court and the initial result of the case was that people whose applications met the original requirements still had their applications granted, but people whose applications would have fallen to be refused were "deferred" until HO decided what to do. From what I can gather, they have now taken the policy decision to
grant many applications that would have been refused under the original rules, even when that decision to grant is of no practical use to the applicant. From the Home Office's viewpoint, this means that even though the COA doesn't, in many cases, allow the applicant to stay any longer than they would have been able to anyway, at least it prevents anyone from taking HO back into court over the COA regulations.
Anyway, that's a bit of background, and I'm sorry to say I think that that is what has happened in your case. The Home Office has taken the "easy" way out (from their point of view) and left you with a COA that is of no practical use except as a means to increase their bank balance.
Really sorry to be the bearer of bad news - and I hope someone will come along and offer an alternative - but my only suggestion is that your other half returns to Brazil ASAP and puts in a "proposed civil partner" visa application....
