Mom passed away with no will in Georgia

She was married but separated and living with me for 4 years due to poor health. She had no will and no money, no debt. We would like to just allow her husband to keep his property and we would like to just have the house we grew up in that is mortgaged in her name only before they married after the death of my father. So since all parties are in agreement as to how to deal with all property and he just wants to sign over the house to us since he can't afford the mortgage. Do we have to go through probate or since he probably has legal right to everything she had, can he just transfer ownership to us in a more simple legal manner? 

Thank you!