This is easy. He is asking for 'flextime'.
Best approach is not to make an issue of it. Create a timesheet or get a time tracking application and start logging start and stop times.
Break times are interesting.. do you clock out to get a coffee for 5 minutes or clock out for a 10 to 20 minute break?
Definitely log everything in your favour. Start times. Stop times. Time for work on the weekend.
Do up all of the paperwork for time worked over normal hours. Keep it with you. Have a lawyer review it if needed. Prepare everything to make a claim for everything.
This is not to actually make a claim. This is to get the PHB off your back and protect your job. Do not ever show this until you are backed into a corner or handed your papers.
Keep going with your current work. Get everything in writing. Make sure you record or get records of your yearly review. Get it all in writing.
What this employee is asking for and is doing is acceptable. The problem is that it can go downhill.
I did much the same years ago. I was formally reprimanded for turning up 30 minutes after everyone else, even though it was within the company policy. My previous manager stepped in and pointed out that I regularly worked until 6pm. End result was not pretty. Some manager are just assholes.
Find out what the expectations are in your workplace. Try to align with them.
You would be surprised how often arrival and end time equates to work done regardless of actual work done