Since never. Level 7 users have been able to do it for the past several years (relocate ANY question). Otherwise, only the user that posted a question, is able to relocate it.
The ability to relocate questions was provided to Level 7s to help ensure questions were posted in the correct category for their topic and it was (mistakenly) assumed that any user that had been on the site long enough to reach Level 7, was likely a quality user and responsible in their behavior on the site (after all, they made it that far without getting their account suspended permanently).
Unfortunately, as with EVERY other feature of the site that can be abused, it has been seriously abused. In some cases, it's quite chronic (the malicious and inappropriate relocating of questions). Yahoo had a way for users to easily report question moving abuse. Verizon Media has given us no such avenue and doesn't appear to be interested in putting a stop to it (or maybe they are working behind the scenes to stop it and just haven't shared it with us, which would be the norm).