Yes. Upgrading really old php application (v4? really?) to v8 is such a big step it will need much dedication, so many things changed between 4 and 5 its not easy. And even upgrading 5 to 7 may break so many things. I would not like to switch with him.
> Adding tests for an app with no documentation requires a lot of effort.
code tests yes. Assuming it's a web app, probably not too hard. Get something that records the browser interactions, and do the common tasks people do (log in, click links, make a report, etc). Having general things like that automated to ensure you can run them repeatedly to make sure basic stuff didn't break unexpectedly will help provide some confidence when making changes.