There are 2 types of JSA, income based and contribution based. She certainly isn't eligible for invome based if her partner works fulltime:
"If your partner or civil partner works 24 hours or more a week on average, you can't usually get income-based JSA (contribution-based Jobseeker's Allowance isn't affected). If they work less than 24 hours, it may affect how much you get
Contribution-based Jobseeker's Allowance
You may get this if you've paid, or are treated as having paid, enough National Insurance contributions (NICs)"