Jim doesn't look up from the screen, but he does give a faint, knowing smile.

The searches he runs come up empty, with the women who do match the description all with easily found records that haven't been falsified. (Of course he can tell. He even takes the time to explain it to Matilda.) It wouldn't be unreasonable to conclude that Agatha Trunchbull is highly unlikely to be working at any school in the UK at the moment, but that's not quite the same thing as a guarantee.