Can one perform the Fajr Qunut during the final Tashahhud for someone who remembers they did not perform it while they are sitting for the Tashahhud?

As long as you did not remember the Qunūt in the Fajr prayer until after sitting for the final Tashahhud, then it is too late to make it up, and it is not prescribed for you to perform it at that point. Your prayer is valid, and you are not required to perform the prostration of forgetfulness (sujūd as-sahw).