Translation:If I die, you will assume the duties of captain.
I assume the captain is speaking. Wouldn't he/she be speaking of him/herself in third person by saying "the captain"? The "duties of captain" is about the duties of a rank, whereas the "duties of the captain" is more about the duties of a person. I think the former is more appropriate if the speaker is the captain, though the latter isn't wrong.
If the speaker was the captain, then wouldn't they say "my duties"? Talking about youself in the third person is strange, at least to my ear. I assumed that the speaker wasn't the captain, but might have assumed the duties of the captain at some point in the past.
Ranks don't have duties, positions have duties. The commander of a ship is called the captain regardless of if they have the rank, and whoever assumes that job will become the captain.
You're technically right, I meant position not rank. But I'm assuming that the captain is talking to someone (presumably his or her first officer) he's giving a battlefield promotion to, in the event of the captain's death in the upcoming undoubtedly glorious battle, so rank and position are the same here.