Since it runs linux, it is possible. It should be a "samba share".

This is a full guide about Samba in GNU/Linux.
https://wiki.archlinux.org/index.php/samba

Install the package (if it is not already) with:
apt-get install samba

And then follow the guide to configure it. It requires to read a lot, but it is easier than it seems.

The shared route should be the external HDD, of course. You can set a fixed mount if "it works sometimes but not always" using /etc/fstab (easy to do), but probably you won't need it.

I hope it helps.