Firstly, congratulations on completing your internship and reaching the final round of interviews!
In your context, a recommendation from a partner you've worked with can certainly be advantageous. While it may not technically be a 'referral' in the conventional sense, it still carries significant weight. Essentially, the partner would speak to your skills, competencies, and suitability for the full-time position, reinforcing your candidacy.
How this typically works is the partner would either speak to the interviewers or the recruiting team before your final round, or write a formal recommendation that is added to your application file. This can give the interviewers additional context and positive information about you before they meet you.
Remember, however, that while having a recommendation is certainly beneficial, it's your performance in the final round that will ultimately determine whether or not you receive a return offer. Make sure you prepare thoroughly and showcase the skills and qualities that make you a strong fit for the BA role.
Best of luck in your final round!