Step 1: Start from the mammal case for comparison.
In mammals, B lymphocytes get their name because they mature in the bone marrow, and the letter "B" first stood for bone marrow.
Step 2: Ask what plays that same role in birds.
Birds do not rely on bone marrow for this job. They have a separate lymphoid pouch near the cloaca called the Bursa of Fabricius, and this is where the letter "B" for B cells actually first came from historically, since it was first studied in birds.
Step 3: Explain what happens inside the bursa.
Immature lymphocyte precursors travel to the bursa, where they mature into functional B cells capable of making antibodies later in life.
Step 4: Eliminate the other options.
The kidney filters blood and forms urine, the keel is a bone on the bird's sternum used for flight muscle attachment, and the heart pumps blood. None of these three organs are lymphoid tissue and none produce lymphocytes.
Final Answer:
B lymphocytes in birds are produced in the Bursa of Fabricius, option (2).