The artifact is the "ebony elephant" which you dig up at Kaya Forests. (see related question)
Dig up the ancient artifact (an ebony elephant) where the tortoise was sleeping. The Kaya Spirits appear and ask you to recover their fingo. Take the artifact to nabooti, swap it for the fingo, and return to the Kaya Spirits.
To get the ancient artifact on Nabooti Island, you need to solve the puzzle in the museum by rearranging the tiles to match the pattern shown. Once you solve the puzzle, you will receive the ancient artifact from the native chief.
The order of acquiring the jewels makes no difference, and the two items (phone, ancient artifact) are not related at all. (see the related question)
The ancient artifact is the carved Ebony Elephant that you dig up at the Kaya Forests. You will need a shovel and a cactus fig (Opuntia Fruit).To get the shovel, go to Blue Nile falls and get the Egyptian Blue Lily. Swap it for a turban at Nabooti and goto Giza, where you will be given a shovel.To get the Opuntia Fruit, climb the trail at the Mountains of the Moon, and see the woman picking figs.Once you have these, use the Opuntia Fruit to lure the sleeping tortoise at the Kaya Forests. Dig where he was sleeping and you will find the artifact.
Dig where the turtle sat and you will find an artifact there (the ebony elephant). The Kaya spirits are seeking their lost "fingo". Go back to Nabooti, to the lady who trades ancient artifacts, and trade the elephant for the Fingo. Take the fingo to Kaya and you will receive the Green Jewel.
Give the artifact (ebony elephant) to the trader at Nabooti who will give you the missing "fingo" (talisman). Return the fingo to the Kaya Spirits to get the Green Jewel.
If you get a shovel and get the turtle to move, you can dig up a carved artifact at the Kaya Forests. The "ebony elephant" is buried directly under the tortoise. (see related question)
There is a Golden Vase on Time Tangled island, which is hidden in a cave at 831 AD and needs to be returned to 328 BC. There is the "fingo", an urn-shaped artifact, on Nabooti Island.
You trade them with the second lady after you get off your blimp
You need the shovel at the Kaya Forests to dig up the Ebony Elephant, an artifact that you can swap at Nabooti for the missing "fingo". Returning the fingo to the Kaya Spirits gets you the green jewel. (see related question)
Nabooti is an island on Poptropica.
The three traders are all at Nabooti, where you first arrive on the island.