**Core Concept**
Libman-Sacks endocarditis is a form of nonbacterial endocarditis associated with systemic lupus erythematosus (SLE). It is characterized by the deposition of immune complexes on valve leaflets, leading to inflammation and damage. This condition is a classic manifestation of SLE's cardiac involvement.

**Why the Correct Answer is Right**
The patient's symptoms and laboratory findings are consistent with SLE, a chronic autoimmune disease. The presence of recurrent arthritis, skin rash, and glomerulonephritis, along with positive ANA and anti-double-stranded DNA antibodies, supports this diagnosis. Libman-Sacks endocarditis is a well-known cardiac complication of SLE, often presenting as a new-onset heart murmur. The murmur is typically due to the formation of sterile vegetations on valve leaflets, which can lead to valve dysfunction.

**Why Each Wrong Option is Incorrect**
**Option A:** Mitral valve prolapse is a condition where the mitral valve leaflets bulge into the left atrium during systole, but it is not associated with SLE or immune complex deposition.

**Option B:** Myocardial infarct refers to the damage caused by a lack of blood flow to the heart muscle, usually due to coronary artery disease. It is not a direct consequence of SLE or the patient's symptoms.

**Option C:** This option is a duplicate of **Option B** and is therefore incorrect for the same reasons.

**Clinical Pearl / High-Yield Fact**
Libman-Sacks endocarditis is a classic example of a "great imitator" in medicine, mimicking other conditions such as infective endocarditis. However, the absence of positive blood cultures and the presence of SLE-specific antibodies should raise suspicion for this diagnosis.

**✓ Correct Answer:** A. Libman-Sacks endocarditis