Co-author wants to put their current funding source in the acknowledgements section because they edited the paper
In general, I would be pragmatic about this. If the contribution of the Assistant Professor is large enough to warrant co-authorship (which is a different story altogether, and not the question here), it should be large enough to mention their funding source. Presumably they have actually had to invest some amount of time into the manuscript to warrant co-authorship, and if they "used" their own university-funded research time or some external project time to contribute to the paper is really their own business.
Clearly this does not mean that you need to pretend like the entire work was funded by your co-authors grant, but a clause in the acknowledgements such as "Prof. X acknowledges the financial support provided by XYZ" is common and completely appropriate.
I'm wondering if putting that acknowledgement would implicitly say that the co-author's current funding also funded the research in the paper.
Only if you word it poorly.
Maybe "Co-author was funded by Blank to edit the manuscript" is a middle ground?
This sounds very uncommon to me. I would only write it like that if you also explicitly list who paid for all other parts of the study (which would be highly unusual in my field).
In either case is it acceptable to "use" this money to edit manuscripts from previous work done and funded elsewhere?
That's a question between your co-author and their funding source, and shouldn't really be your concern.
If you have valid reasons to be worried about the implications of such insinuations (something I'm not sure about) - you can write it a longer comment describing two phases of the work - the "research" you mentioned to which said co-author has not been part of, and the writing work. Now, I wouldn't say co-author X was only involved in writing, or only involved in editing, but perhaps something like:
Lab research was conducted at
[Institute name]between[start year]and[end year]and supported by[funding sources here]. Work on this submission has received additional support from[the editing co-author's funding source here]
There are several questions being asked here. One primary question is:
I'm wondering if putting that acknowledgement would implicitly say that the co-author's current funding also funded the research in the paper.
Before worrying about this, it might be worth asking what the consequences would be if someone were to make this mistake. (I can't answer that question.)
Presumably the primary grant that funded the work has reports, and the reports for that grant will properly attribute this paper.
Presumably the co-author will not lie when reporting to their granting agency about what their grant supported on the paper. (But, it may be listed on the grant report.)
If the grant is a recent grant, and the work is clearly older than the grant, then it would be clear that the particular grant couldn't have funded the research.
A secondary question is:
is it acceptable to "use" this money to edit manuscripts from previous work done and funded elsewhere?
- You'd have to look at the terms of the grant to determine this. In the US, professors are often funded in the summer by grants, and they can sometimes be interpreted rather broadly. So, if the professor worked on the paper during the summer, then it would be correct to list the paper as supported by the grant.
As for advice on what to do:
I would hesitate to list the activities that were funded individually - at least in my field this sort of detail is never/very rarely provided.
But, perhaps you could divide the funding by the people who were funded by it: Authors X, Y, Z were funded by Grant A, author X was additionally funded by Grant B. Author W was funded by Grant C. This might give the delineation you are looking for.