Your 3D object looks like each arm is shaped irregular, meaning that the edge lengths won't be the same, meaning that the UVMap cannot be the same, if you want a map without stretching. However, if you just want each point to be identical, you can indeed achieve this by unwrapping in a strict order.
First, select one of the corner faces (remember which one!) on one of the four islands, and press L when the mouse cursor is over the matching island. Choose Seams as the limiting factor. Then, reset the UVMap. This will take each quad and set the UV coordinates to (0,0), (0,1), (1,0) and (1,1), no matter what the shape in 3D is.
Next, use Follow Active Quads as the unwrapping method. The active quad is still the one which was selected first, and its current UV position serves as the starting point for the follow active quad unwrap.
Next, select the corresponding face and island from the three other shells. I'm marking them in the GIF here before I unwrap the rest. This is important so the orientation of the resulting UV Map is identical to the others. The four resulting UV islands will have completely identical vertex positions, but, as stated initially, stretching for sure.
If stretching is not desired, all you can do is match up the boundaries of your map by snapping vertices. Snapping to vertices also works for scaling, as you can see in this little GIF here: