Letter of support for promotion to full professor from an "unusual" student
The department asked you to write because they want your opinion.  Of course they also asked others.  If they do not ask you specific questions, then just give the reasons for


  I am super happy to be able to support her/his promotion because I have a great opinion of her/him and I genuinely think s/he deserves that,  


If they do include specific questions in their letter to you, then answer those, or explicitly say "I cannot answer question 3 because...".