I got a letter from my sister. According to her letter, she's doing well at the moment.
Literal
Younger-sister [from-から] news [subject-が] existed. Letter [according to-によれば] currently well [hearsay-だそうだ].
便りがあった ('received word') uses 便り for personal correspondence. によれば ('according to') marks the source of the information. 目下 (もっか, 'at present/currently') is a formal time expression. だそうだ marks hearsay.