Please don't forget to mail the letter.

Literal

Not-forget-[without-ず] letter [object-を] mail-[polite-request-てください]

投函 (とうかん) is the formal/written verb for 'depositing into a mailbox' — literally 'throwing into a box'. In casual speech 手紙を出す or ポストに入れる is more common; 投函 carries a business-letter or postal-service flavor.