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Tyler Nii, 27, from California, has not been seen since Wednesday and is presumed dead following the incident.
His male instructor, from the skydiving company NZONE was rescued from the water 20 minutes after the incident with only minor bruises.
NZONE voluntarily suspended business but today the company's website was open for bookings and spokesperson did not deny they were operating.
The police dive squad will begin searching the lake for Mr Nii's body tomorrow.
The police have previously said recovering the body of Mr Nii would be complex because the water where he fell is 250 metres deep.
The police are looking at using sonar technology to help locate the body.