How to argue with postdoc hired for a project, to work on tasks from another project

You can switch her to another project if you have the funding for it. What you cannot do is to have her work paid by one H2020 project to carry out work for some other separate project. If that's what your postdoc says, she is right.

However, even in your existing project, there should be sufficient leeway to do work on good publications, research etc. and improve the work that you have carried out on the core project. Research never stops.

Alternatively, if you have funding for another project, then you can ask for the budgets to be reassigned (Edit: if she agrees) so that she is paid through the budget of the other project. That's perfectly acceptable, albeit you may have to return some of the budget of the original project she was hired for if that is not used in its entirety.

What you cannot do is to have the original project budget pay for work carried out on another project.

I'm just guessing, but she probably has the right of it. I would cease arguing with her entirely but suggest that something additional might be done on the original project that might also result in additional publications, etc.

Don't be the bad person here. And, especially, don't find some way to punish her for being both competent and ethical.

Funding agencies usually understand that circumstances may change during the life of a project and have the ability to authorize changes in the project’s scope. A postdoc finishing all her predicted goals ahead of schedule seems to me like one of those situations where such a change is certainly justified and desirable.

I suggest that you write to the program managers of the program that funds your project. Describe the situation and the alternative project you are proposing to reassign the postdoc to. Ask (as an informal, hypothetical question at first) if they would allow a change of scope of the project to authorize this reassignment. If they say yes, you can show the postdoc this pre-approval - it mostly counters her argument that the reassignment is unethical or illegal (perhaps still leaving a bit of room for argument, though, depending on the laws in your local jurisdiction).

If she then agrees to the change, you can go ahead and obtain formal authorization through whatever formal process the funding agency requires you to go through, if such a formal process is required (typically filling some web form on the funding agency’s grant management website and having the program manager submit approval on their side, something I had to go through once or twice).

Now, if upon your initial request the program managers don’t want to authorize the reassignment, well then you have your answer, even if it’s not exactly what you wanted to hear.