This answer was given by Paul Pladijs. I just took his commands and made a git alias for convenience.
Edit your .gitconfig and add the following:
[alias]
mergetheirs = "!git merge -s ours \"$1\" && git branch temp_THEIRS && git reset --hard \"$1\" && git reset --soft temp_THEIRS && git commit --amend && git branch -D temp_THEIRS"
Then you can "git merge -s theirs A" by running:
git checkout B (optional, just making sure we're on branch B)
git mergetheirs A