Which phrase best fits the meaning of having received an award after much effort?

The phrase "Having been awarded after much effort" directly encapsulates the idea of receiving an award specifically as a result of significant effort. It explicitly mentions the act of being awarded, which aligns perfectly with the context of the question. Furthermore, the inclusion of "after much effort" reinforces the idea that the recognition is not just a random occurrence, but rather the fruit of hard work and dedication.

In contrast, the other phrases do not convey the same clarity and precision regarding the connection between effort and recognition. "Having been recognized for their efforts" suggests acknowledgment but does not specifically indicate an award being given. "Having celebrated their victory" implies a sense of triumph but lacks reference to the effort leading to that success or the aspect of receiving an award. "Having worked hard towards success" highlights the notion of effort but does not indicate any outcome or recognition, such as being awarded. Therefore, the chosen phrase most accurately reflects the intended meaning of receiving an award after significant exertion.