Faça do terminal:
sudo apt-get install apt-file
Então, depois que ele for instalado e você atualizar as listas:
apt-file search mbstring.h
E esta é a saída que retornou para mim:
mingw-w64: /usr/amd64-mingw32msvc/include/mbstring.h
mingw32-runtime: /usr/i586-mingw32msvc/include/mbstring.h
php-doc: /usr/share/doc/php-doc/html/book.mbstring.html
php-doc: /usr/share/doc/php-doc/html/intro.mbstring.html
php-doc: /usr/share/doc/php-doc/html/mbstring.http.html
php-doc: /usr/share/doc/php-doc/html/ref.mbstring.html
php5-dev: /usr/include/php5/ext/mbstring/mbstring.h
wine1.0-dev: /usr/include/wine/msvcrt/mbstring.h
wine1.2-dev: /usr/include/wine/msvcrt/mbstring.h
wine1.3-dev: /usr/include/wine/msvcrt/mbstring.h