It is really sad to see this happening.
Although I don't know what kind of collection they hold, it looks like they seem important documents regarding the Portuguese immigration in Hawaii, maybe original documents?
I will suggest for this material to be donated to the State Library and Archives, at this level the chances for them to survive through the years are bigger. There they will have the opportunity to be treated regarding conservation, digitized and become an open source for historians and researchers like us. Today the main goal of Libraries and Archives is Outreach!
I just made a quick search and they have a very big online collection, including Portuguese genealogy:
Isabella Baltar