How do I declare that fact during the interview when asked?
Must note that you should mention that not when, but if asked.
No need to elaborate much on it, in fact your current phrasing on this post reads good to me: Mention that you parted ways because both sides had different expectations from the role, but that you ended up in good terms.
You could also consider including your former manager's phone somewhere on the part where you describe that past job experience on your CV, given that she said it's ok for you to share in case they need a reference.
Update: Reading more closely, seems that you worked there for just a few weeks. In that case, given it was such a short experience, I concur with Justin Cave and would not advice including it on your resume.
Not only it was a really short time, in which you perhaps didn't learn/do much, but including it may raise more eyebrows and questions than have a positive impact on your chances of landing a new job.