One way of finding a box in one grid that is the same as (or equivalent to) another box in the second grid is through the laborious process of mapping or matching the digits in one box of the original puzzle to the digits in another box of the equivalent puzzle.
For example, let us find out which box in twin B is equivalent to box 7 of the original puzzle (twin A).
First let us map box 7 (twin A) to box 1 (twin B). Then we shall get a one-to-one mapping between the digits of the two boxes.
1. Mapping box 7 (twin A) to box 1 (twin B)
2 --> 6
8 --> 8
What is left is mapping for box 8 and box 9 (twin A).
Just find the mapping for box 8 (twin A) is enough.
box 8 (twin A) --> box 2 (twin B)
3 --> 1
1 --> 8
8 --> 9
2 --> 6
Box 8 (twin A) is not equivalent to box 2 (twin B).
As the above mapping is invalid, let us map box 8 (twin A) to box 3 (twin B)
1 --> 6
3 --> 4
8 --> 3
2 --> 5
Box 8 (twin A) is not equivalent to box 3 (twin B).
Therefore, box 7 (twin A) is not equivalent to box 1 (twin B).
2. Mapping box 7 (twin A) to box 2 (twin B)
7 --> 8
4 --> 7
1 --> 6
What is left is mapping for box 8 and box 9 (twin A).
Just find the mapping for box 9 (twin A) is enough.
box 9 (twin A) --> box 1 (twin B)
7 --> 9
1 --> 6
Box 9 (twin A) is not equivalent to box 1 (twin B).
As the above mapping is invalid, let us map box 9 (twin A) to box 3 (twin B)
4 --> 6
2 --> 3
1 --> 7
Box 9 (twin A) is not equivalent to box 3 (twin B).
Therefore, box 7 (twin A) is not equivalent to box 2 (twin B).
3. Mapping box 7 (twin A) to box 3 (twin B)
7 --> 6
2 --> 7
4 --> 9
1 --> 5
What is left is mapping for box 8 and box 9 (twin A).
Just find the mapping for box 9 (twin A) is enough.
box 9 (twin A) --> box 1 (twin B)
7 --> 9
1 --> 6
Box 9 (twin A) is not equivalent to box 1 (twin B).
As the above mapping is invalid, let us map box 9 (twin A) to box 2 (twin B)
4 --> 8
2 --> 9
Box 9 (twin A) is not equivalent to box 2 (twin B).
Therefore, box 7 (twin A) is not equivalent to box 3 (twin B).
Hence the bottom block of rows in twin A is not equivalent to the top block of rows in twin B.
In other words, the bottom block of rows has not interchanged position with the top block of rows in the same grid to form an equivalent puzzle.
And in other words, the bottom block of rows may have interchanged position with the middle block of rows in the same grid to form the equivalent puzzle.
The bottom block of rows may even has not shifted at all!
The next step is to continue the laborious process of mapping box 7 (twin A) to box 4. box 5, box 6, box 7, box 8 and box 9 of twin B.
Though the process is laborious, it is the sure way of finding the equivalent boxes and, of course, the solution. Note that this process involves logical deduction. I leave it with anyone who is interested to continue the laborious process on their own.
The second method is to try to spot any digit that has appeared twice or thrice in a block of rows (columns) in a grid and then map them to the other digits that have appeared in corresponding cells in a block of rows(columns) in the other grid.
For example, in the middle block of rows in twin A, the digit 8 appears in all the three boxes. This is a trial and error method, but you may be able to locate the equivalent boxes very fast if you are lucky to choose the right boxes for comparison in both grids.
