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Good morning. There can and could likely be a problem. The reason why I say this is because short sale transactions require the purchase to be at arms length. This situation is anything but that, since this is your fiance and you are giving her the down payment, so if the lender finds out about this, there could be problems and they may refuse to sell. She will likely be asked to sign a document, at some point, advising that she does not know you or have any relation to you and if she lies and there is fraud, she could be liable and there could be issues. Seeing how they may ask to see the source of the downpayment as well, there is expose and you both need to know that when proceeding.
The issue is with the short sale being at an arms length transaction. If she wants to buy a home in her name only, that should not be an issue. The issue is going to be her buying your home, as your fiance, through a short sale, with you giving her the money. This is exactly what the lender wants to avoid. The reason being is that you will be getting out of the home, someone will be buying it for less then what is owed and then you will be gaining a legal interest in it. Also, FHA loans are typically given to first time home buyers, so I am not sure how both loans are going to be FHA, but you lender may be able to clarify that. Seeing how the second loan requires 20%, that would be a conventional loan, not FHA, so the first may only be FHA which requires only a small down payment of around 3%
I just wanted to follow up and see if you had any other questions or needed me to clarify something. I am here to help, so please let me know. Thanks!