Well that one won't fit. Different "innards" entirely as it's for a Colt SAA clone and there's no guarantee the basic mounting screw locations will be right. Probably won't be. With a LOT of work you might be able to get it up and running but it would be a major pain at minimum.
One caution: technically this isn't a "Bird's Head" grip frame, it's a "Thunderer/Lightning" pattern. It's based on the stock grip frame from the earliest Colt DA revolvers of 1877 and a bit later. It's really not period-correct for SA revolvers but I believe SASS tolerates 'em .
The caution is this: the original Colts these were designed for was chambered in fairly low powered rounds, esp. by today's standards. At some point this sort of grip frame will try and split your hand in half under recoil. Exactly where that is depends on the shooter of course. Most people can shoot SASS-grade 45LC with it no sweat. Somewhere around the high end of the 44Spl's power range, and almost certainly if you shoot very hot heavy 357s, you won't be happy with this thing. However, shot to shot control with ammo it can cope with is reputed to be pretty good.
Ruger's "Bird's Head" is very different, and has a rep for surprisingly strong recoil control - certainly able to handle more than this critter if it fits your hands at all.
So. Be aware of the recoil handling limits of this design. Within it's limits it's great.