Git subtree split a directory into new repository

gistfile1.txt

Imagine this project structure

proj_a/
  lib_b/ ... contents you want to split

First create a new git repository somewhere in the file system

  mkdir /lib_b
  cd /lib_b
  git init

  # Allow pushing to currently checked out branch
  git config receive.denyCurrentBranch ignore

  # back to proj_a
  cd /proj_a

  # Setup remote
  git remote add lib_b /lib_b

  # Split the history for lib_b subdirectory and push into lib_b remote's master branch
  git subtree push --prefix=lib_b lib_b master

  # ... handle further changes in /lib_b, with full history for that module