They verified Linear B against a new tablet that turned up in a dig after the Kober/Ventris* solution had been published. It had pictures of jars with no or one or two handles, and the claimed Linear B for "two handled jar" and such next to the correct picture.

* Ventris' publication, but given Kober's contribution to the work they should really share equal credit. I like to think Kober would have got there on her own if she had access to the larger corpus that Ventris had (the Pylos tablets) and a comparable amount of free time and money available.