Medicaid Transfer Assistance Required

My mother is 103 years old. She has madicare and madicaid (in Maryland). She is in the hospital right now, and she needs to go to a long term care facility. There is a nice facility (non profit) in DC sponsored by a church would like to take her. But her madicard is in Maryland. Would you please help me transfer her Madicaid from Maryland to Washington DC? She have a DC residence to use. How long does it take from MD to DC? How much I need to pay the lawyer fee?