Answer:
No, only this experiment is not enough to prove that transformation has taken place.
In the original experiment by Griffith, IIR and IIIS bacteria were used. Here the student has used IIS and IIR bacteria. There might have been a mutation in IIR strain due to which it got converted to IIS strain and killed the mice. So first he needs to set up a control of only injecting IIR bacteria into mice and prove that it alone can not kill the mice.
Also, he did not demonstrate that the heat killed all the IIS bacteria. Some might have survived and killed the mice. To check this, he needs to inject the mice with heat killed IIS bacteria and check if it is still able to kill them or not.