I think you should tell the truth. That she moved in with you, but was not on the lease.
Pull her credit report and see if your address shows up as her current address on it.
https://www.annualcreditreport.com/index.action
This will show that she's been living with you. As a manager, when I pulled credit reports, I always checked the current and previous addresses listed. I did this to see if the info on the application matched it, and if there were any missing addresses that the applicant didn't want me to know about. This could indicate a bad landlord review.
In your case, it would show that she did live with you.
Then, when I call the landlord up and ask for a reference on the two of you, he may say, I know Joe, but I don't know anything about Suzie. And I'd say, well, they say they've been living together in his apt. And he's say, Oh really? And I'd say, did they cause any problems? Did they pay the rent on time? And hopefully, he'd say, No, no problems, and the rent was always paid on time, but I don't know anything about this Suzie person.
Then, I'd know that 1) you didn't tell the LL she moved in; but 2) there were no problems.
This would tell me that you two have been successfully co-habitating, and you were so low-key that the LL didn't even know she was living there.
And then, if your other stuff looked good (income, credit, her other landlord reference), I'd very likely rent to you.
Good luck!