Step 1: Pick out the core feature. The man holds fixed false beliefs of infidelity (his wife is having an affair) and persecution (people talk ill of him, a friend abroad helps the plot). These are well systematised delusions held for 2 months.
Step 2: Note what is absent. There is no thought disorder, no hallucinations, no inappropriate behaviour, and the rest of his mental life and personality are normal.
Step 3: Apply the criteria. Persistent (delusional) disorder is defined by one or a set of related, non-bizarre delusions lasting at least 3 months (the ICD threshold), with personality and functioning otherwise preserved and no prominent hallucinations or formal thought disorder. The picture fits this exactly.
Step 4: Rule out the distractors. Schizophrenia would need thought disorder, hallucinations, or odd behaviour, which are absent. Paranoid personality disorder is a lifelong pattern of suspiciousness, not discrete fixed delusions of recent onset. Acute and transient psychosis comes on abruptly and is usually polymorphic and short, not a stable single-themed delusion lasting 2 months.
Step 5: Therefore the best fit is Persistent delusional disorder. (Duration here is just under the formal cut-off, but among the four choices this is clearly the intended and correct diagnosis.)
Answer: Persistent delusional disorder.