Complete question:

I have been in service for more than half a year, but less than half a year ago, my employment has been switched to JAM!. This means I would be hired less than a year ago, and therefore don't have the right to receive an unemployment benefit. How do I solve this?

You will be judged on the last 36 weeks of working, and that's not restricted to JAM! only. You're entitled to a WW benefit if you have worked during 26 weeks in the last 36 weeks. You can include your entire employment past and also the hours that you've built-up with employers that preceded JAM!.