Backup and rescue
Trainers are saved in this browser, on this device. Nothing is on a server, so clearing browsing data or switching browser loses them. Download a backup and you can put a trainer back at any time.
You are at …. Saves belong to one address — if he played somewhere else, restore it there.
A missing trainer is usually in the other browser profile. Chrome keeps separate storage for each profile — the avatar at the top right. The same address signed in as a different person is a different set of trainers, and this page cannot see across. If someone is missing, check there before assuming the worst. A trainer link, below, works in any of them.
What is stored here
Nothing at all. If he played at a different address, the trainers are there and not here — saves do not travel between addresses.
Back up
A file lives on this computer. A link does not — mail it to yourself, bookmark it, or open it on another machine, and that trainer comes back. It works in any browser and any browser profile.
Restore
This replaces every trainer in this browser with the ones in the backup. Download the current lot first if you want to keep them.