Short answer to How can I effectively rebase B off A so that it looks like B started from A?
Assuming you want to move exactly one commit:
git rebase --onto A B~ B
If you want to move more then one commit use:
git rebase --onto A old_A B
The rest of the answer.
Your branch of B is still around (you can check it out), but its parent is still the exact commit object that A was before.
to see a graphical representation of this I use:
git log --graph --decorate --all
to see all branches and where they are with respect to each other.
What you originally had:
o---o---o---o master
\
o---o---o A
\
o B
What you have now:
o---o---o-----------o master
\ \
o---o---o(B~) o---o---o A
\
o B
In terms of using --onto, you need to have a starting point and an ending point.
use:
git rebase --onto [target] [rebasing stops] [rebasing head]
git rebase --onto A B~ B
And what you get:
o---o---o----------o master
\ \
o---o---o o---o---o A
(old_A) \
o B
[branch_name]~ indicates the parent commit of the branch.
The B~ is the branch that you do not want to change. (It happens to be the old A)
Alternatively, if B was the only commit that had A as a parent, (i.e., B is the end of a chain of commits that branch off master) you could do
git checkout B
git rebase master
git checkout B~ # this is the commit before B (the A commit)
git branch -d A # remove the old A branch (it was rebased, and so is now invalid
git branch A # recreate the A branch on the commit that is based on the original A