The patient had the deadly Ebola fever, but before he died he managed to tell police of the theft.
Officers tracked down a man who had started using the phone, who then confessed to the crime.
The man claimed he had visited the ward to "comfort" patients, though he didn't know any of them in person, district police commander John Ojokuna Elatu told the Sunday Monitor.
Soon afterwards he started showing signs of the disease.
Not a very bright idea.