Once again, the plan involved an unorthodox form of payment.

Olympus, the documents show, proposed a real estate transaction. Olympus would sell two dormitory buildings in Shenzhen to the Anyuan affiliate. The sale price would be set well below the buildings’ market value, according to the confidential report from the Western law firm. The deal would reward Anyuan, but more discreetly than a cash payment.

Senior Olympus executives would have to sign off, and they were nervous. The reports and memos showed a debate ensued between Tokyo executives and the Asia-Pacific office, based in Hong Kong, over who would bear responsibility for the decision. Executives knew about the bribery accusations against Mr. Chen and were concerned about legal risks, according to the documents.

At one point, the Olympus president, Hiroyuki Sasa; chairman, Yasuyuki Kimoto, who retired last year; and two other board members in Tokyo told subordinates in Hong Kong and Shenzhen to move forward with the real estate deal, according to the report by the Western law firm. Managers in Shenzhen were instructed “not to leave any written evidence of the purpose behind the transaction,” the law firm found. Email memos on the matter were labeled “top secret.”

There are conflicting accounts of what happened next. According to the inquiry, Olympus balked at the dormitory sale at the last minute, judging it too risky. But managers in Shenzhen had already signed a deal, which Anyuan claimed contained clauses promising the sale.

In the end, Olympus paid Anyuan 24 million renminbi, or $3.7 million, in cash, through its affiliate An Ping Tai, according the inquiry. Olympus declined to comment on details of its arrangement with Anyuan, beyond saying it was “one of many contractual relationships” it maintained in the normal course of its business.

In August 2014, eight months after its managers signed the deal with Anyuan, Olympus was informed that it would not be fined or otherwise punished for the inventory-recording discrepancy, according to the inquiry.

“In the end, a fine that had been estimated at least 60 million renminbi was not levied at all,” the inquiry found.