he didn't ask whether she can find a job, he asked whether she has rights to work while she is on Family visa and under his sponsorship... so here is the answer:
in order to be able to work, all she will need is a Work Permit, and her husband has to approve it, that's it.
And yes, she can stay under her husband sponsorship, again, if the hiring Company doesn't mind it (some companies insist on transfer sponsorship under their names)

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"What lies behind us and what lies before us are small compared to what lies within us."
Oliver Wendell Holmes