Well..... I guess you could say that inorganic nutrients are often organic byproducts.
Most of the inorganic nitrogen and phosphorus in our systems originate from the organics we feed our livestock.
Other organisms are responsible for that conversion, or break down, not cyanobacteria.
Think of cyano like a tree. A tree can utilize the nutrients in a dead fish as fertilizer, but only after other organisms have converted those organic nutrients into inorganic nutrients that are dissolved in water. The tree has no access directly to the organic nutrients within the dead fish. The fish must decompose first, or be broken down into its inorganic elements. Like nitrogen, phosphorus, iron....................