I graduated with a doctorate, and my tutor asked me to write a thesis. What should I do?
This kind of thing mainly depends on what you think. If it is within your power and beneficial to you, write it! But in the end, it should be reflected in your own achievements, and you can't be taken for yourself by the teacher. If the tutor can't give you any help just for his own needs, it depends on the teacher-student relationship between you and the tutor. In the long run, you have to consider whether the mentor has any influence on your present and future. If you don't want to get into trouble, do your best!