Define what you mean by Directory Module.
Because Applications->Directory is not meant for this. it is designed for use as an option in an IVR to let callers get transferred.
Next, Admin->Asterisk Phonebook was the original location for setting up speeddials.
The problem is that it writes directly to the astdb and is not stored in a simple to access form within the FreePBX framework, but I have a basic python script to pull that into a Yealink XML address book.
Then, the most modern tool within FreePBX is the Admin->Contact Manager
I have wrote a couple different for this.
Finally, if it was just your extensions, I have something for that.