Active - Who  wrote this letter?
​Passive - This letter was written by whom ?
Is this active to passive conversion correct? pls justify

Dear student,

Yes, the conversion is absolutely correct. As per the rules, in active voice our subject is our priority and in passive voice our object on which the action is being done becomes our priority.
Active - Who (subject) wrote this letter (object)? The statement says that our subject did the work.
​Passive - This letter (object) was written by whom (subject)? The statement says that a task was performed on our subject.

Regards