Step 1: Break the nitrogen cycle into its two oxidation steps.
Nitrification happens in two stages: ammonia is first oxidised to nitrite, and then nitrite is further oxidised to nitrate.
Step 2: Assign the correct bacterium to each stage.
Nitrosomonas (along with Nitrosococcus) carries out the first stage, converting ammonia to nitrite. Rhizobium is a nitrogen-fixing symbiont in legume root nodules, unrelated to nitrification. Azotobacter is a free-living nitrogen fixer, also not involved in this oxidation step.
Step 3: Confirm the second stage organism.
The organism that specifically oxidises nitrite to nitrate is Nitrobacter, completing the nitrification process.
\[ \boxed{\text{Nitrobacter}} \]