Mentioning a published paper from a current team member in a PhD letter application I am writing a motivation letter for a PhD position related to antibody analytics. While I was researching the current research group I read a paper published by current team member "A" which I found pretty interesting, and honestly, also quite motivating.

I would like to include this in my motivation letter, but the problem is that "A" published this paper when she was working at another research institute. NOT the one I would be currently applying to.

Would it be a faux pas to mention this paper in my motivation letter?. On the one side it would show that I have actually researched them, and that I am actually motivated (which I explain why). On the other side, it could give the impression that I thought it was published by them, and I was not careful.
I think the content of the publication is more important than the author of the publication.  I would mention the paper as well as other similar papers that you have read that are by other authors.  Most likely, your  person "A" will know of the other authors in your field so it is not necessary to soley focus on mentioning person "A."  I think it is more important to show your interest in the specific research area rather than knowing where person "A" worked.