She finished writing one letter.

Literal

She [topic-は] letter [object-を] one-letter wrote-finished.

一通 (いっつう) uses the counter 通 for letters and written communications. 書き終えました uses the compound verb ~終える (to finish) with the polite past ました. The counter 通 is specifically for letters, emails, and similar documents — distinct from 枚 (flat objects) or 冊 (bound books).