While in Lilycove City, you can find Captain Stern in that museum place where Team Magma/Aqua are standing by. I forgot how to get rid of them, but once you do, you can find Captain Stern in that museum place I mentioned.
Capt. Stern is not in Pokemon Leaf Green. He is only in Pokemon Ruby, Saphire or Emerald.
In the slateport city boat dock place
You go to slateport and you deliver the Devon goods to captain stern.
Go to Mt. Pyre if you haven't already done so. If you have, go to Slateport City and talk to Capt. Stern, and then return to Lilycove City to continue the storyline.
In the Slateport museum.
Capt. Stern is not in Pokemon Leaf Green. He is only in Pokemon Ruby, Saphire or Emerald.
In the slateport city boat dock place
In Pokémon Alpha Sapphire, after you reach Lilycove City, Captain Stern can be found at the Stern's Shipyard located in Slateport City. He is not in Lilycove; instead, players must return to Slateport to continue the storyline involving Team Aqua or Team Magma. The shipyard is where you will encounter him after the events involving the Team's plans.
He's in the museum.
You go to slateport and you deliver the Devon goods to captain stern.
Go to Mt. Pyre if you haven't already done so. If you have, go to Slateport City and talk to Capt. Stern, and then return to Lilycove City to continue the storyline.
In the Slateport museum.
You can either go to the next route or get the exp.share from the president.
It's the Seafloor Cavern... An underwater cave where the legendary pokemon, Kyogre is sleeping.
Once you get the scanner, go to slateport and find captain stern, he will trade you a hold item for it.
Captain Stern is on the top floor of the museum in Slateport City.
Captain Stern will be in the Oceanic Museum. There will be Team Aqua members outside. They will once clear when you go into the shipyard when you will find a man beside a table. Once you talk to him, the Aqua members will be gone and you can enter the Museum for $50. Hope this helps!