The boost came as it also revealed that it could sell a majority stake in the potentially lucrative $2bn (£1.3bn) project.
Rockhopper has said that seven or eight companies were interested in bidding. Among them is cash rich Edinburgh-based Cairn Energy, run by ex-Scottish rugby international Sir Bill Gammell.
Rockhopper could give up its lead role in the Sea Lion field it reckons has 1.3bn barrels of oil.
“Rockhopper would be willing to relinquish operatorship, if the farm-down interest was high enough,” said a note from Morgan Stanley.
The drawback for any deal is that the Falklands is the subject of a territorial dispute between Britain and Argentina.