Final answer:
The ozone layer is part of the atmosphere, fossils are found in the lithosphere, rust can be found in both the lithosphere and the hydrosphere, and cyanobacteria belong to the hydrosphere.
Step-by-step explanation:
The ozone layer is located in the stratosphere (part of the atmosphere), fossils are found in the lithosphere (as a record of previous life on Earth), rust (iron oxide) is a chemical compound that often forms on the lithosphere but also can be found in the hydrosphere, and cyanobacteria are typically found in aquatic environments and thus are part of the hydrosphere.
Accordingly, the matches are: 1) ozone layer - atmosphere, 2) fossils - lithosphere, 3) rust - lithosphere or hydrosphere, depending on where it is located, and 4) cyanobacteria - hydrosphere.