The oil explorers had suspended work on the first well of their 2015 drilling campaign on April 24 after the technical issue.
While the problem was being fixed, the drilling rig undertook work at the adjacent Chatham and Jayne East wells, the two companies said on Tuesday. Both wells were suspended when the rig was ready to return to the Isobel Deep location.
"The Isobel Deep well is expected to take approximately 15 days to complete," said Falkland Oil and Gas in a statement.
Oil drilling in the area remains controversial due to an ongoing sovereignty dispute over the islands between Britain and Argentina.
Argentina has filed a domestic lawsuit against the drillers, saying their activities are illegal. (Reporting by Karolin Schaps; Editing by Mark Potter)