If the repos are in different organizations on GitHub you can fork one and create pull requests cross forks from the GitHub interface.
But if you want to create pull requests between repos from the same organization on GitHub, you can edit the remotes on the original repo (Repository A in your example) and then "send" branches cross GitHub repositories and create the pull requests using GitHub interface.
Check my answer on git fork repo to same organization
for more details.
Also, please note that this is only possible if Repository A and Repository B share at least part of commit history, otherwise you will just get a message like:
repositoryA/new-feature
and repositoryB/master
are entirely different commit histories.
When you try to create the PR.