The UK family initially refused entry to New Zealand after the death of their son at sea is praising the kindness of Jacinda Ardern after she stepped in to help overturn the decision.
Barbara Genda, Harry Jarman and their 13-year-old daughter Amelie were last week granted a business exemption into New Zealand's maritime border by the Ministry of Health.
The family had applied for a humanitarian exemption to enter New Zealand in order to sell their yacht on which they had been living on an around-the-world trip.
The family needed to sell the $1 million yacht in order to have capital to buy a home back in Sussex, and have found it extremely difficult to find a buyer in French Polynesia.
Barbara Genda said last week the border exemption finally came, after they were asked to reapply by New Zealand authorities.
"The praise and huge thanks go out to your Prime Minister and NZ Herald who were willing to listen to our story," Genda said from a remote area of the Society Islands where they are floating.
"We are very grateful for the opportunity to sell the boat in the New Zealand to deliver her to the buoyant market in New Zealand, we did receive more than 'little kindness' from the authorities in their compassionate yet practical attitude to our case."
Genda said there were still a few documentation hurdles required before the family could enter New Zealand, including entry visas, but they hoped they would just be formalities.
They also need to apply for NZ customs permission to enable a formal sale here.
"We are hopeful for a quick sale and have some interest from a buyer already. We are committed to selling and have just lowered the price to $950,000, which is the lowest-priced boat on the market for a comparable make and model," Genda said.
While the family apply for the documents, they are also fighting a legal battle in French Polynesia to prosecute the person charged with manslaughter who was driving the speedboat that struck and killed their son Eddie.
"We have, however, a more pressing issue here in French Polynesia, where the criminal manslaughter case is not progressing favourably," Genda said.
"We might need to stay a little longer until some progress is made and we can be assured that justice will be served for our son. This may delay our departure until December.
"Our big concern is to ensure that the criminal case against the driver who killed our son is not forgotten in French Polynesia as soon as we leave here.
"We are determined to seek justice for our son whose death was so senseless and preventable."