Sync Outlook calendar with somone who wont download the outlook application or the caldav syncer addon

I work with somone who uses outlook live via their web browser exclusivley, and they refuse to download any extensions, addons, or do anything beyond accepting an invitation for a shared outlook calendar.

I need to sync a calendar with them. I have an outlook account, but for security reasons (no i cant clarify) I cant not install any microsoft stuff on any of my machines although I can use a VPS I have access to do command line stuff like with vdirsyncer.

Any advice or help would be greatly appreciated