Given that GitHub doesn't allow to push files larger than 100 MB, it is not possible to git clone and push a repository with large files into GitHub enterprise. The push fails with a:
remote: error: GH001: Large files detected. You may want to try Git Large File Storage - https://git-lfs.github.com.
remote: error: File large.zip is 145.00 MB; this exceeds GitHub Enterprise's file size limit of 100.00 MB
(N.B.: there is a repository importer, but this is only for github.com, and requires public access to your repository)
Fortunately, GitHub provides support for storage of files larger than 100MB since April 2015. So how to convert a current repository with such large files into a GitHub LFS compatible repository I can push to?
You can now use git lfs migrate built-in command to both assess which files is best to migrate and also do the actual history-rewriting.
See git-lfs migration tutorial for more details.