How can I move the answer to a proper question without copy-pasting it? It is important to me that the original author of the answer retains credit for it.
Just Copy/Past it, or provide a link to the origonal post, or both.
You could just ask the author to re-post their answer under the second question. That seems like the simplest, low-tech solution.
I doubt Jeff has a special tool to let you re-link the actual answer.
If it's not your answer, and you don't have the reputation to edit other's answers (currently 2000) it is sometimes still possible to see the markup for an answer.
If the answer has been edited so that it has an edited X timeunits ago link, you can click on that link to view the revision history and then click the view source link to open a new tab/window with it in.
If it hasn't been edited then you can still view the revision history, but you'll have to manually enter the url in your browser's address bar. Click on the link link for the answer to get it's unique number in the anchor of the url (after the # character) and then go to the url:
Once you've got the markup you can copy and paste it to another question, crediting the original author and providing a link back to the original answer.
(And if anyone is concerned about whether it's right to duplicate an answer, all the content contributed to the site is done so under the Attribution-Share Alike license as stated in the FAQ and it's worth duplicating as the original answer may eventually be deleted if it's not relevant to the question.)
Pose a new question with the answer as an insightful one (giving attribution of course).
Maybe then someone else will have a better answer and it'll get up-voted and everyone wins.