New tenant doesn't have security deposit

[Sol G.]

Hi all, A woman that lives in Florida applied for my apartment in New Jersey, because she's coming back to live with her husband who live in New York (and works in NJ). I was supposed to sign a lease today with a new tenant. When speaking with the tenant last week I told her that she needs to pay before she moves in the first months rent plus a 1 1/2 month security deposit. The tenant told me that she understood from me in the first time we spoke that just one months rent is for security deposit and she only prepared that. I told her that I'm making an exception this time and she'll pay me the rest of the security deposit with the next months rent. Her Husband arrived today to sign the lease with no money, ( he had given me a months rent for the deposit to hold), I asked him for the rest of the funds, he said that he was told that he would be able to pay it in installments so he would only have it next week Friday, after phone calls back and forth with his wife who said that she understood it from me like her husband said. So my question I'm standing here in a dilemma what to do, should i give her till next week Friday and let her move in before she pays security or I shoul