Crediting work
The first point is that the student should have discussed authorship with Professor Pi long before this event. If the student is working for Professor Pi, the professor certainly should have access to the data developed by the student.
However, the student should talk to Pi since there would not be a loss for the grant if it were written to identify the student as an author, since the purpose is to continue the work done by one of the professor's students.
There is little range of "acceptable variation," although there is a range of practice. The only acceptable practice is to fairly credit work done.
To whom the presentation was made is not relevant. If my student does good work under my direction, I get some of the credit as the advisor but should not attempt to take the most credit unless I really did most of the work.