Two of the three parties that objected to the Ansbacher application in the Cayman courts earlier this year have decided not to appeal the decision.
Confidential documentation has been sent by the bank to two of the objectors - Cayman trust companies Hamilton Ross Co Ltd and Poinciana Fund - so it can be reviewed before it is handed over to Irish High Court inspectors.
Mr Barry Benjamin, the businessman who controls both companies, has reviewed the documentation identifying personal names, initials and company names, which he believes should be removed in order to protect the identities of account holders.
He has also asked that information concerning transfers to jurisdictions outside the Cayman Islands be removed as it would allow the inspectors establish who had received the funds.
The Chief Justice of the Cayman Islands, Mr Justice Anthony Smellie, ruled last month that Ansbacher Cayman Ltd should disclose information to the inspectors concerning the business it conducted with Irish clients but that it should edit the information so clients are not identified.
Mr Benjamin said a significant amount of documentation had been reviewed by him and that he was expecting more from the bank shortly. It is not clear whether Mr Benjamin will be given an opportunity to review the extent of the deletions made before the documents are handed over to the inspectors.
He said the documentation he had reviewed was mainly bank statements and it supported the bank's contention that it carried on normal banking business with its Irish clients. The documentation is understood to go back to the 1980s.
Hamilton Ross and Poinciana Fund managed funds for Irish clients within the Ansbacher deposits.
A third legal team, which objected to the Ansbacher application, is known to have represented another Irish client or clients of the bank. It is likely this party or parties will also be given an opportunity to review documentation before it is sent to the inspectors.
A spokesman for the Department of Enterprise, Trade and Employment said he did not know if the inspectors had yet received any documentation following last month's decision of the Cayman courts. "The inspectors will not comment on any part of their investigations," he said.
In his ruling, the Cayman judge decided that, if the inspectors wanted, they could submit questions about any of the accounts disclosed in correspondence with Ansbacher.
Mr Benjamin said he was "satisfied" with the ruling because it stated that information that would identify clients should not be given to the inspectors.
The bank, which was concerned about negative publicity arising from being seen not to co-operate with the inspectors, is said by some sources to be content with the ruling.
The Tanaiste, Ms Harney, said she did not think the ruling was helpful but she remained confident the inspectors would produce a substantial report.