will the prosecutor drop my criminal case?

I was falsely accused of stealing someone's money from her bank account by impersonating her and having known her passwords, whereas, this person was the one who linked her personal account to my business account (she was my bookkeeper and second signer on my accounts). When I went online to check my accounts, I saw that I had three different accounts like a checking and two savings. I withdrew the amount from what showed up as one of my own accounts and closed that account. Subsequently, This person went to the police and accused me of stealing her money as we were living in the same house, that I must have known her password. This person never explained to the police that she was my bookkeeper, that she took out my money and put it in her account, that she was the one who linked her account to mine. Prosecutor doesn't know about linking accounts. Should I show him?