I have found the instructions
here on moving to a new host, but it looks a bit intimidating to my limited skillset and I have a (probably dumb) question.
Both the old host and the new host have Cpanel, with Installatron. I am running the latest version of phpBB. The domain name is staying the same, but the file paths within the hosted space will change.
Would it simplify the job at all to use Installatron to install a fresh instance of phpBB on the new host? Could I just 'restore' the old backups into the new host, then make a few corrections?
Or am I better off just following the instructions in the linked article word for word?