I have a couple of Drupal 6 sites using the Webfm module (https://drupal.org/project/webfm). This module was never migrated to Drupal 7 because in this last version of Drupal the file API changed completely, and the module would have to have been rewritten completely, and nobody did it.
My solution was to substitute the webfm module by the "Elfinder" file manager and corresponding Drupal module (https://drupal.org/project/elfinder). This does not substitute all the document manager features of webfm, it is just a file manager and has no database management of the documents, but on the other hand it is really good as an editor. So maybe I will complement it in the future with some "knowledge base" module to search and put metatags to my documents.
First of course you have to migrate your Drupal 6 site to Drupal 7. Enable all the modules in Drupal 7, you will not be able to enable webfm because there is no Drupal 7 version, but the tables of webfm will be in your migrated database.
Installing and configuring Elfinder in your migrated Drupal 7 site is easy, and it can use exactly the same file struture left over by webfm. You will also have to link it to your editor, in my case CKEditor, that was also easy.
The problem comes with the links that webfm created (of the type "/webfm_send/#" where # is an arbitrary number assigned by webfm.) If you don't want to end up with zillions of broken links in your site you have to fix those. If you have few nodes you can fix the broken links by hand, but then it's unlikely that you were using the webfm module at all, as a small site can work perfectly with a flat file system without any special document management.