I had read this case before in a collection of crime stories.
Dr Lloyd tells about the time he was in the Canary Islands. In his hotel she saw a lady and her companion, Miss Mary Barton and Miss Amy Durrant. The following day something terrible happened. One of the women, Amy, the companion, drowned even though her employer tried to save her. Amy had no family but some relatives in Australia. There was a woman that claimed that she saw Miss Barton forcing Miss Amy’s head under the water, but the matter was left there. Miss Barton left.
Some time later Dr Lloyd read in the newspaper that Miss Barton had drowned in Cornwall. Her clothes had been found, but not her body. She left a suicide note, confessing to some crime, which Dr Lloyd thought it referred to Miss Amy’s murder. Those at the table try to come up with the reason why Miss Barton had wanted to kill her companion, but none of the explanations was satisfactory. Then Miss Marple guesses the truth when she tells that the woman who was killed was not Miss Amy but Mary Barton, and since no one knew the women’s identities, Amy passed herself off as her employer. Dr Lloyd says that as luck would have it, she ran into Amy Durrant in Australia, and there he learnt the truth. Amy was the eldest of a big family, and they were related to Miss Barton who refused to help them. So Amy travelled to England, and under an assumed name she was employed by her cousin, who she killed, and then she faked her death so she and her siblings could inherit Miss Barton’s money as her next of kin. Dr Lloyd says that he did not report the crime because it was clear that Amy didn’t have long to live, and she actually died six months later.