She replied to my letter right away.

Literal

She [topic-は] my letter [to-に] immediately reply [object-を] sent.

よこす is a somewhat old-fashioned, slightly curt verb meaning 'to send (toward the speaker)' — its tone shifts notably with context. In negative or pointed contexts it often carries a faintly resentful undertone; here, paired with すぐ ('right away') and a positive past, it sounds appreciative — she replied promptly. The に marks the letter as the target of the reply (the recipient, the speaker, is implicit). すぐ is the bare adverb; the alternative すぐに carries the same meaning but is slightly more bookish.