(I am posting this for advice regarding somebody else’s problem, but for simplicity, let me pretend it's me. To clarify misunderstandings in the comments: I am asking on behalf of my partner and can supply any additional detail as needed; I am fully informed.)
I have conducted a research near the start of my PhD studies, which I have since quit. This was collaborative work with another PhD student (who has also left since then) and my/our supervisor. We had an agreement regarding the authorship of the paper: I, as the person having done most of the work, would have been first, followed by my classmate, and finally our supervisor.
Some time has passed since then, I have quit the programme, so did my classmate, but we have only got around to publishing the paper now.
Today, I received an email from my supervisor that since both of us students have left the faculty and are not planning on continuing our studies there, he proposes a change to the authorship of the article, making himself the first author, as (I paraphrase) even though I have done most of the work, it would have not been possible without his financial and infrastructural support. There is some truth in this argument, but as I said, authorship was already established.
I do not think it is fair to alter the order of authors merely because we are no longer affiliated with the institution; we were at the time of writing and the relevant research work.
The paper is already finished and is just waiting to be submitted. I am willing to take part in creating a second revision if requested by the journal upon review (and have made this clear to my supervisor).
Naturally, I have begun negotiating with my supervisor (and the 3rd author) in the matter, but I would like to ask: if my supervisor refuses to give up the place of the first author (I must add that I believe he in fact did very little work), what are my options to resolve the situation?
UPDATE To clarify further confusion in the comment section: the paper in question is a complete, finished manuscript, ready for submission. The reason this whole thing is happening now (several months after we have finished working on it) is that it has already been submitted to another journal previously and was eventually rejected. This is a resubmission to another journal.
There has been no change to the contents of the paper. The supervisor has done no additonal work (such as ‘picking it up as a draft and completing it’). He had very little input in the entire process.
I believe he wishes to change the author ordering because we no longer ‘need’ publications (having quit the academic career at least for the time being), whereas he does. It would not be the first time he claims other people’s work as his own, but this is not relevant for this post.
UPDATE 2 Unfortunately (and unsurprisingly to me) it does not seem that our (former) is cooperative in the question. Upon reaching out, he offered to alter the name order, moving me up to the place of second author, but still keeping himself as first, if and only if I agree to handle the entire submission process. In addition, he has brought up omitting me as an author altogether?? That said, I do not wish to abuse SE for a blog sharing my experience with this problem. I will continue attempting to reach an agreement with my supervisor (and the 3rd author) and potentially escalate the problem to my uni’s ethics office or similar if there is no way to handle this locally. I plan to include update the post with a final conclusion to let future readers possibly facing such a problem see how it can be resolved.