Has this person you want to hire already accepted the job at the partner firm? If not, she is behaving ethically by seeking to work with you. She's expected to maximize her pay and job satisfaction while looking for a job, as long as she doesn't break promises.
You didn't mention the reason your organization interviews people who join partner firms. Does your org have the right to blackball people if they do poorly at your interviews, even when a partner firm has already decided to hire? Is your purpose to help partner firms decide wisely? Is this a way to help potential employees understand their jobs better?
At any rate, if the interview you do is a genuine interview and not some kind of training exercise or sham interview, it's clear that your company, your partner firm, and the candidate are all open to having the outcome of the hiring decision changed as a result of your interview. Fitting a candidate to the best job for her is in fact an excellent outcome.
It's possible that the agreement by which you do this interviewing for partners implies that you should not grab the partner firm candidates. So, it may be that you are "poaching" this person if you hire her. But you're not doing anything dishonest. It should not damage your business relationship.
If it's a serious issue your organization can make this right by offering to pay your partner firm the cost of finding and recruiting this candidate. Or, you can send other qualified candidates to that firm.
What will damage your relationship is keeping secrets from the partner firm. Please don't try to do that. It won't work for long. Also, please don't try to force the candidate to take a job that's not ideal for her. That never works out well for long.