**Core Concept**
The question is testing the student's knowledge of a diagnostic test used to detect residual Helicobacter pylori (H. pylori) infection, a common cause of peptic ulcers and gastritis. H. pylori infection is typically diagnosed using a combination of clinical history, endoscopy, and laboratory tests.

**Why the Correct Answer is Right**
The correct test for detecting residual H. pylori infection is the **13C-urea breath test**. This test involves the ingestion of a small amount of 13C-labeled urea, which is then metabolized by H. pylori's enzyme urease. The resulting 13CO2 is detected in the breath, indicating the presence of H. pylori infection. This test is non-invasive, sensitive, and specific for H. pylori infection.

**Why Each Wrong Option is Incorrect**
**Option A:** The **serum pepsinogen test** is used to assess gastric mucosal atrophy, but it is not specific for H. pylori infection.
**Option B:** The **stool antigen test** is also used to detect H. pylori infection, but it is less sensitive than the 13C-urea breath test.
**Option C:** The **endoscopy with biopsy** is a diagnostic tool for visualizing the stomach and duodenum, but it is more invasive and expensive than the 13C-urea breath test.

**Clinical Pearl / High-Yield Fact**
The 13C-urea breath test is a useful tool for monitoring the effectiveness of treatment for H. pylori infection, as it can detect residual infection even after treatment.

**Correct Answer:** B. Stool antigen test