Is it permissible to use gifted money designated for studying for another matter related to studies, or must it be returned to the donor?

You are required to spend the money given to you to complete your tuition payments for the purpose intended by the giver. However, if the giver did not intend to designate it specifically for tuition, but rather it was given informally as a general assistance, then you may spend all or part of the money for purposes other than paying tuition. The matter depends on the giver's intention, as Zakariya al-Ansari explained: If he intended for it to be spent on a specific thing, then it is designated for that; otherwise, it is not designated, and the recipient owns it and may dispose of it as he wishes.