What is the ruling on writing an inaccurate declaration for master's degree registration? Is it considered forgery? Does it invalidate the obtained certificate Islamically, and what are the consequences of that regarding salary acquisition?

It is not permissible to write a statement that contradicts reality, and one must repent from it. However, this does not mean that everything related to it or resulting from it becomes null and void. Studying is permissible, and the prohibition here is due to a temporary cause. The person who did this must repent from lying in his statement. As for the master's degree and the job resulting from it, they are not forbidden. Some universities prohibiting simultaneous enrollment in two programs is a legitimate organizational matter and does not contradict seeking knowledge.