Final answer:
The best evidence that DNA is responsible for the transfer of the phosphorescent trait would be the observation that descendants of the living strain that acquired phosphorescence also display the trait, indicating that the information for phosphorescence was incorporated into their genetic material and inherited by subsequent generations.
Step-by-step explanation:
If the ability to fluoresce is a heritable trait, the best evidence to support that DNA passed from the heat-killed, phosphorescent strain of bacteria to the living nonphosphorescent strain would be that the descendants of the living cells are also phosphorescent. This outcome would suggest that the phosphorescent trait was incorporated into the genetic material of the living strain, allowing it to be passed to subsequent generations. Griffith's transformation experiments demonstrated that heritable information could be transferred between cells through DNA. Later, the Hershey and Chase experiments further established that DNA, not protein, was the material that carried genetic information by using bacteriophages labeled with radioactive isotopes. When 32P (which labels DNA) was used, it was found inside the bacterial cells, indicating that DNA is the genetic material. If proteins (which could have been labeled with 35S) had been responsible for transferring the phosphorescent trait, then we would not expect this heritability in the descendants.