Actually this happened in my office. One of my office namazi who performed Zuhr prayer in factory mosque with jamat and then he went to some other mosque and led Zuhr prayer. Is it alright, if not then people who have offered prayer behind him do they have to offer prayer again as they do not know about this.
بسم الله الرحمن الرحيم
If he performed first salah with the intention of Zuhr (Fardh) salah with jamah and then led the jama’at of Zuhr salah in other mosque, then the salah of those who performed Zuhr salah behind him was not valid and thus they will have to reoffer their salah; since the second salah was nafl for him and those who perform fardh should not follow one who offers nafl.
Allah knows Best!
Darul Uloom Deoband