Rewriting old commits in the master branch

Say I have this commit history:

A - B - C (master)
         \
          D - E - F (Feature)

I'd like to amend commit B. So, I do:

git checkout master
git rebase -i <hash of A>

After the rebase is done, I see the change using git log. However when I switch to the Feature branch, commit B is still as it was before the rebase. In other words, when I'm in master branch, the commit history looks like this:

A - B' - C (master)

When I switch to Feature branch, the commit history looks like this:

A - B - C (master)
         \
          D - E - F (Feature)

I understand that rewriting the commit history is not wise, but I have to do this in my case.

How can I amend an old commit and have those changes be reflected on every branch? Am I doing this the wrong way?

The new commit history will be force pushed into Github and I don't want to mess things up.

Any help would be appreciated.

Solution

After your rebase, what you actually have is

  B'- C' (master)
 /
A - B - C
         \
          D - E - F (Feature)

So now to complete the operation you'd have to rebase Feature on (the recently rewritten) master

$ git checkout Feature

$ git rebase master

          D'-E'-F' (Feature)
         /
A - B'- C' (master)
 \       
  B - C - D - E - F (soon to be garbage collected)