My father is currently working in America, but he sent us a letter last week.

Literal

Father [topic-は], now America [at-で] is-working [but-が], last-week letter [object-を] sent-toward-us [polite-ました].

送ってきました uses ~てくる to mark the letter as arriving toward the speaker's location. が connects two clauses with a slight contrast: though he's far away, he still wrote.