Is it permissible to buy a gift for a teacher instead of paying the overdue financial amount for his lessons, if he has become a friend and might be embarrassed to take the money?

You must return what is due to its owner or seek his forgiveness, for the Prophet, peace and blessings be upon him, said: "The hand is responsible for what it has taken until it returns it." The fact that he is your friend does not waive his right.

If you fear embarrassing him, then look for an indirect way to return what is due to him, such as sending it with another person without mentioning your name, or presenting it as a gift. The important thing is that the full right reaches its owner by any means, so that you may be absolved, unless he absolves you of it.