I can think of three possible solutions or workarounds.
One workaround is to have students save their website into one zip file and upload the zip file to a Forum or Database
activity. Other students could then download
the zip file, open it on their own hard disks and view it 'off line'. Not ideal, but it would work.
Another possibility is to either give students their own course in which they have editing rights, and they could then create a 'web site' within a moodle course, or within an existing moodle course they could be given editing privileges over the Web Page resource module. This requires the ability to override roles
, and so needs moodle 1.7 or greater. It would also be a rather limited web page.
Another possibility is the Wiki activity module.
None of these solutions are perfect, but they might work for your colleague.