In the unit summary table for the AFFS on page 134 of First Succession War, the First Arcadian Cuirassiers are listed as being on Galatia III in 2786 at 100% of full strength, and in 2821 they're still listed as being on Galatia III, but at 41% of full strength.
Galatia III is described on page 28 as being one of three Hegemony worlds the FedSuns annexed in 2785, and shows up on the map on page 44 as being one of the worlds conquered by the Draconis Combine between 2786 and 2791. The map of the various AFFS counterattacks from 2801 to 2818 show Galatia III as a system that the AFFS hadn't recaptured by 2818, and on the map of the Inner Sphere on 2821 on pages 112-113, Galatia III is a Combine system, with the FedSuns having recaptured Mallory's World by 2818 and then lost it again by 2821.
So... should the Arcadian Cuirassiers be listed as being on Galatia III in 2821? I've not checked exhaustively, but I can't see another example of an AFFS unit being listed as being on a world belonging to another faction in 2821, and I can't find anything in the text that would suggest that the Cuirassiers managed to hold out on Galatia III for 30-35 years, so I'm not sure if the Cuirassiers' entry is possibly in error?