Nylva said while work was beginning to take place in Colombia, it had been slow to start.
She said the family’s appeal had been taken up by a man living in the country, who had become a “rock” and a “godsend” to them.
According to Nylva, the man contacted the General Attorney’s Office, which prompted movement in the case.
“We’re now getting a bit of feedback as to actually what they’re doing,” she said.
A Foreign, Commonwealth and Development Office spokesperson said: “We are supporting the family of a British man reported missing in Colombia and are in touch with local authorities.”
A GMP spokesperson said: “We have been in touch with Anton’s mother, and we have dedicated officers that have been deployed to maintain contact with the family and provide any updates should GMP receive such from overseas.
“We understand this is frustrating for Anton’s family, and we are working to find them the answers they desperately seek.”