Maybe add a banner to point to the web archive of the previous site? Life moves on and domains are ultimately rented much like our time here. Having a new business doesn’t stop you from honouring that, in my view.
Take the time to take snapshots in whatever appropriate method to archive his site, spawn a new static site under the name of "rememberingjoebloggs.whatever" and add a banner to your own site at his old domain at the top saying that you are honouring his life by keeping the site alive at a different address.
Then go and post on Hacker News what you've done and then contact some journalists who want feel good filler content.
Just make sure the person wasn't on a sex offenders register or anything else that would be brand damaging by association.