Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
As long as you received the fellowship by lawful means without cheating or forgery, then you have the right to benefit from it till the end of that program even if you completed your studies. This ruling is effective provided the authorities or the rules and regulations do not make it a condition that the beneficiary has no right to use it after completing his studies.
It is better to inform the authorities that you have completed your studies and the scholarship is still coming to you and then act in accordance with their approval. They are giving you the grant, thus you must not cheat them and should inform them of the reality. The Prophet (Sallallahu Alaihi wa Sallam) said: "whoever cheats is not one of us." (Muslim)
Allah knows best.