How is your job share split? Ie. what days do you work, does he/she work?
Just wondering as I know the way I have worked with both of my job share partners has had to change depending on the days/schedule set up between us.
I don't know if this would work for you, but my current job share & I jointly plan everything for termly/weekly plans, and then each plan our own days. She then sets up for me on days she is in the day before me, and I set up for her on her day when I'm in the day before. (She works Mon, Tue, I work Wed, Thur and we work alternate Fridays, so I would prepare her Mon or Fri work for her, and she would prepare Wed for me). By plan, I mean she leaves her daily plan ahead of time, and I change it as necessary depending on what I've got through, and I make sure that everything is set up for her the next day. She does the same for me.
We also make sure we leave handover notes or phone each other on handover days - it is the person who is finishing their days that has the responsibility for this rather than the other having to chase for it the next morning. This works really well as we both rely on the communication.
However, we were very fortunate that for the first year of our job share, I was in school on all of her days as I taught two classes at the time, so our planning and processes built up over that time and work really well now.
How feasible would it be for you to try to have face to face sessions for a while? I realise these would be unpaid and that doesn't work for everyone depending on childcare etc.
I think you may also need to go to management if this doesn't improve. You can't be expected to carry your jobshare partner in the long term this way. It lets you and the class down.