https://www.gov.uk/family-permit
"Stay after your EEA family permit expires
You can stay in the UK after your permit expires if you:
are the family member of an EEA national - see if you’re eligible
qualify for a ‘Surinder Singh’ application
have a retained right of residence
have a derivative right of residence
You can apply for a residence card card or derivative residence card to confirm your right of residence. You don’t have to apply but it will make it easier to prove your right to live and work in the UK."
Fairly long application form to fill out, EEA FM, normally takes 6 months to process so your partner will be without her passport until it's sorted out. But will get her rights to work (CoA) document within 2 weeks.
Optional 5-year valid card that will cost £65.