To keep their work, the best way would be:
# current dir is ~/oldversion
# create a new directory
mkdir ~/newversion
# get the clean versioned project
git clone git@github.com:Your/repo .
# create a new local branch and go on it
git checkout -b migration
# now copy everything from the old project. the modified files will appear with "git status"
cp -r ../oldversion/* ./
# commit the last work
git commit --all -m "importing to git"
# now, make some checks/editio, git diff, git rm, git revert, git checkout path/to/file whatever
...
# then import your work in a branch for everyone, if you use master that means
git checkout master
git merge migration --no-ff -m "migrated by me"
If a scm was used, you may prefer to exclude some files at one point, like the .svn directories.