。
Don't forget to mail this letter.
Literal
Forget-not-[continuing-で] this letter [object-を] post [imperative-なさい].
Same ~ないで + なさい structure: 'without forgetting, [do X].' 投稿する technically means 'to submit/post' (to a publication or online), whereas mailing a letter would more naturally use 投函する or ポストに入れる. The word choice gives this sentence a slightly off-register feel.