Yes! I just closed on a house in September, co-signer is a citizen though. It was hell. I had to inform the lenders who kept telling me it was not possible. It was an FHA loan, 3.5% down payment.
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Date Application Sent -8/18/12
The Lockbox the application was sent to - Dallas Lockbox/Nebraska
Mailing Method (Express, priority, certified) etc. - USPS Express Date delivered - 8/20/12 Biometrics-9/17/12 Approved I-765: 10/31/12 Yay! I821-D Approved 11/1/12