If you know from which branch your "given branch" has been created, then making a patch is easy:
git diff master Branch1 > ../patchfile
git checkout Branch2
git apply ../patchfile
(and you can generate a patch applicable without git too)
But finding the right "creation commit" of a branch can be complex: see "Finding a branch point with Git?"
The OP akirekadu used:
git format-patch $(git merge-base --fork-point master)..branchB
You can see it used in "git diff
between working copy and branch base"
legends2k adds in the comments:
One can verify the generated patch with git apply --stat patchfile
This won't apply, but give the details of the patch.
Warning: AGP notes in the comments that:
$(git merge-base --fork-point master)..branchB
command may not find the correct branch root revision every time
ijoseph points out in the comments
Incidentally, Phabricator handles this kind of stuff seamlessly by automatically generating those patch files for each push.