WE have no idea if brother's documented income, or credit, would allow him to get a HELOC.Brother could get a HELOC (home equity line of credit). The house would be appraised, she can get her 50% and quit claim her share over to him.
Although if I were him, I'd ask she pay for the costs of the HELOC and reimburse her 50% of the property taxes he paid on the property (since he paid 100%).
Doing business with family is always fun!