The rise of oxygen concentration in the modern atmosphere is partially due to the preservation of organic matter before it could

I would say the word would be "decompose". Organic matter for example trees, large ferns of bygone eras etc acted (and still act) as a carbon sink and if they are preserved, they to some extent keep carbon dioxide out of the atmosphere so help to keep oxygen levels higher in the atmosphere. Some forms of preservation are rapid burial and the formation of fossils of ancient organisms.