how to change commit author in whole git tree, not only 1 branch

Question

there are questions with answers about how to change committer's email of each commit in a branch. but how to do it in a whole tree? i want to change A -> B in the following repo:

Branch 1        Branch 3   Branch 4
 |                  |      /
 B   B (Branch 2)   B  _ B
 | /                | /
 B                  B
  \____   _________/
       \ /
        B
        |
        A
        |
        B
        |
        A
        |
        :
        :
        |
        A