However during a follow up inspection, that addressed the violations in the investigation, Smith stated to Jones that this has not been done

However, during a follow-up inspection that addressed the violations in the investigation, Smith stated to Jones that this has not been done.

However, during a follow up inspection that addressed the violations in the investigation, Smith stated to Jones that "This has not been done".

I agree with joypulv.

"However" is an interrupter and needs a comma after it. "Follow-up" is a compound adjective and needs a hyphen. There's no comma after the first "that." Quotation marks are not needed after the second "that." The sentence gets a period at the end.