Drilling will take 32 days to reach the planned depth of 3336m.
Waggamba-4H is about 150m from the Waggamba Plant tie-in point.
CS Energy has pre-paid $3.5 million for drilling the well in PL 202 and, in return, will receive 50% of gas production and 35% of the associated free oil and condensate production.
Meanwhile, the surface flowline to connect the Fairymount-9 well in PL 46 to the central oil storage tank has been completed.
The downhole rod-insert pumping string will be installed by the end of this week.
According to Mosaic, the well is expected to be on pump for the production test of the sub-unit B Sand within two weeks.
Fairymount-9 is about 300m north-northeast of Fairymount-4, which has produced to date over 205,000 barrels of oil.