The phrase "asserts he has been" is correct and usable in written English.
It can be used when someone is stating or claiming something about their past actions or experiences.
Example: "The witness asserts he has been present at the scene of the crime."
Alternatives: "claims he has been" or "maintains he has been".
Indeed, Mr. Cuomo's aides asserted, he has been aggressively campaigning across New York, raising money at a faster pace than Mr. McCall, and in recent months winning such key endorsements as that of Steven Pigeon, the Erie County Democratic chairman.
Mailer could fairly assert he had been both cursed and blessed by early success, but he was mostly blessed.
Mr. Kennedy, in an earlier statement televised nationally, asserted he had been driving Miss Kopechne to the ferry and had lost his way and that his car had gone off the bridge into a pond.
Asimov was sufficiently upset that he later obtained token payment from Wollheim so that he could assert he had been paid for his story.
Postol asserts that he has been continually rebuffed by the MIT administration, most recently by Hockfield.
But though he asserts that he has been working hard with coaches, he still has trouble with basic things, like breath support.
THIS is the legend of Mr. Harrison: At his 1982 trial on weapons charges, when the prosecutor asserts that he has been running guns for six months, Mr. Harrison, in a grand heroic stance, orders his lawyer to set the record straight.
Imagine a phlogiston theorist who, upon hearing of the success of oxygen theory, claims that his theory has been vindicated; he asserts that he has been talking about oxygen all along but just by a different name.
"It is not evidence capable of supporting or asserting that he has been a sexual predator for 40 years".
He railed at the "Russian bear" for its war in Chechnya, where Mr. Putin has asserted that he has been fighting terrorists trained in Mr. bin Laden's camps and financed with Al Qaeda money.
