"I'm getting weaker every hour but I'm never losing hope as God is with you now. Come home," she wrote.
Photos on her page show Mr Efremychev holding a newborn baby, which were captioned "father and son time".
The incident is the second in the Rodney area in recent months.
On October 14 Stewart Atutahi, 37, from Snells Beach and 22-year-old Nicholas Stubbs from Warkworth went missing after setting off in a fibreglass boat from Martins Bay.
Mr Atutahi was skippering the boat and his body and wreckage of the vessel were found soon after the men were reported missing.
Mr Stubbs' body was found on November 1 near Kawau Island in the Hauraki Gulf.
The deaths have been referred to the coroner.