But an Immigration manager said in response: "While Immigration could appreciate the concerns outlined, many applicants are in a similar situation."
Another letter to the agency written by Mr Finlayson himself in July 2010 reiterated that the applicant was living in a refugee camp.
Mr Finlayson advised the agency of the difficulties in keeping a job offer open for the applicant and sought an update.
He was told the application was 13th in the capped managed queue, and that the agency had to adhere to an instruction "which determines the order and manner" of processing applications.
A case officer was allocated only in September 2010 - 19 months after the lodgement.
"The application was still being processed three and a half years later when a complaint was made to me in July 2012 about INZ's delay in reaching a decision," Chief Ombudsman Dame Beverley Wakem said.
"I have formed the opinion that INZ unreasonably delayed in processing the application, and failed to take into account the humanitarian factors favouring prioritising it."
Following a provisional opinion by the Chief Ombudsman to Immigration, the applicant and his family were approved for permanent residence.
However, the agency continued to argue that other similar cases should not be similarly prioritised, Dame Beverley said.
"I recommend that INZ puts in place processes to ensure that priority is given to all residence applications from persons facing particular hardship or deprivation." Dame Beverly also included those in "a critical life or death situation".
The agency was also asked to ensure all current and future applicants in such situations were "dealt with on a priority basis".
Immigration spokesman Marc Piercey said the agency was working on providing further guidance for prioritising cases since the ruling.
"Immigration instructions already provide for prioritisation on a case-by-case basis," Mr Piercey said.
"Immigration has maintained a good working relationship with the New Zealand Security Intelligence Service, which completes national security checks, and is confident that it will be able to come to a working agreement with respect to the Chief Ombudsman's recommendations."