Frame this by the question: which disorder gives durable, organised false beliefs in a man who is otherwise intact? The vignette stacks up jealousy ($delusion\ of\ infidelity$) and persecution (he is being talked about, a far-off accomplice aids the scheme), and these have run for two months without budging despite reassurance.
The diagnostic lever is the company the delusion keeps. Here it travels alone: no voices, no muddled thinking, no disorganised conduct, normal personality, normal day-to-day life. That isolation of a single delusional theme on an otherwise clear mental landscape is the signature of delusional disorder.
Test each alternative. A man with schizophrenia would also show hallucinations or formal thought disorder; this man shows neither. Paranoid personality disorder is a stable, lifelong suspicious style present long before, not a fresh circumscribed delusion. Acute and transient psychosis is abrupt, shifting and brief, unlike this steady single-theme belief.
So the only option that matches a lasting, well formed, non-bizarre delusion with everything else preserved is persistent delusional disorder.
\[\boxed{Persistent\ delusional\ disorder}\]