She told me to write a letter to one of her friends in Germany.

Literal

She [topic-は] me [to-に], Germany [in-に] is-existing friends one-of [to-に] letter [object-を] please-write [quotative-と] said.

An embedded request — the polite ~てください is preserved verbatim inside と言った, giving the listener the speaker's exact words rather than paraphrasing. The relative clause ドイツにいる ('who is in Germany') sits before 友達 because Japanese stacks all modifiers before their noun. 友達の1人 ('one of [her] friends') uses の partitively to extract a member from a set. Letter-writing carried more cultural weight when this kind of sentence was a common textbook drill — a friend abroad meant handwritten correspondence and international stamps.