AMP Australia told her it would not be offering transtasman superannuation portability until at least the end of next year.
"It seems to be astonishing that one of Australia's largest fund managers and iconic institutions, which has a subsidiary in New Zealand offering KiwiSaver funds, is not willing to do this," Lawson said.
AMP Australia confirmed that it had no immediate plans to get on board with the portability scheme.
"The transtasman portability scheme came into effect on July 1, 2013, however participation in the scheme is not compulsory. We are currently assessing the legislation and haven't yet confirmed timing for implementation of the transtasman portability scheme in Australia," a spokeswoman said.
AMP said it did not know how many of its super customers were New Zealand citizens.
In New Zealand, all the major KiwiSaver providers are already offering transtasman portability.
Vedran Babic, operations manager at Fisher Funds, said the firm had received a number of requests from members but a few Australian fund managers were not releasing savings.
"Some are already saying 'we're not opting in'. There are definitely a number of issues to iron out."
Babic said there seemed to be a lot of confusion and invited clarification from industry bodies.
Inland Revenue said it was aware of some Australian schemes which had been rejecting members' transfer-out requests.
While it was voluntary for schemes on both sides of the Tasman to accept transfer-in funds, it was compulsory to release funds if a member requested, said spokesman David Miller.
"New Zealand officials had been made aware that some Australian schemes did not know about the new requirement to transfer out funds to a KiwiSaver scheme, and have rejected members' transfer-out requests.
"New Zealand officials have been liaising with the Australian authorities to ensure they make appropriate guidance available for Australian scheme providers," Miller said.
The Association of Superannuation Funds of Australia said the large majority of its regulated funds would allow transfer out to a KiwiSaver account.