I worked as the lead for a project (that involves other sites) for 3+ years. I got the project up and running. The project is now completed, but I was unwell towards the end of it and writing got delayed by 2 months. I had a collaborator who served more like a co-ordinator at another center. This collaborator took over during the time when I was unwell (summarized the final set of results). Now wants to share first authorship with me, and has started writing up the work. I do not think this is a fair call. How can I diplomatically tell this collaborator 'no' without damaging relations with this collaborator as well as higher ups?
This is a decision which needs to be made by the project manager and perhaps by a senior person in the management chain, if you are unwilling to make it yourself. They are the ones who approved the project, who provided the budget for it and who will benefit from its success or it will suffer from its failure it that does occur.
You should consider not making too great a deal about this whatever decision that they ultimately make. Unless this is the largest project that you will ever work on in your career, then sharing credit shouldn’t be that important to you. There will be other projects and if you demonstrate that you are a “team player” you’ll be able to helm those and receive as much praise and acknowledgment as you may need.
If you do make too much of a furor about this relatively minor issue, you may be labeled a troublemaker,petty or not a team player. These labels will be difficult to rid yourself of and most people choose not to work with people who have a reputation of being difficult, WHile that may not be “fair”, the world as they say is round,not fair.
Allow this person to accept some credit for the project and look to be the gracious professional that you certainly wish to be seen as being,
It sounds like the other person has done a fair amount of work and is also contributing in the writing efforts. Is there another way to acknowledge this person's contribution to the project? What kind of acknowledgement would you expect if you were the other person? It's too bad you became unwell and needed assistance - is it not good that this other person was available to help?