Is it permissible in Islamic law for a female colleague to call her male colleague to wake him up for studying, given that there is no other conversation between them and she is the only one who helps him with that, knowing that their communication is limited to study-related matters?

Speech and communication between non-mahram (definition) men and women without a significant need is a gateway to fitnah (temptation/strife) and can be a gradual enticement from Satan. Some scholars have explicitly stated that it is not permissible for a man to speak with a non-mahram young woman without a need. Therefore, it is not permissible to correspond with this girl or to ask her to wake you up. Instead, you can set an alarm or ask a male colleague to do so, and limit study-related communications and calls to male colleagues.